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  • 1
    Electronic Resource
    Electronic Resource
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 107-137 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 2
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 47-82 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 3
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 1-18 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 4
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 139-151 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 5
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 153-179 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 19-46 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 197-224 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 225-253 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 255-287 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 83-106 
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 289-317 
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    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 12
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 181-195 
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  • 13
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 319-380 
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  • 14
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    Palo Alto, Calif. : Annual Reviews
    Annual Review of Computer Science 1 (1986), S. 381-450 
    ISSN: 8756-7016
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
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  • 15
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    Oxford, UK : Blackwell Publishing Ltd
    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: The Coach system, a computer simulation of a human tutor, was constructed with the goal of obtaining a better understanding of how a tutor interprets the student's behavior, diagnoses difficulties, and gives advice. Coach gives advice to a student who is learning a simple computer programming language. Its intelligence is based on a hierarchy of active schemas that represent the tutor's general concepts and on more specific information represented in a semantic network. The coordination of conceptually guided and data-driven processing enables the Coach system to interpret student behavior, recognize errors, and give advice to the student.
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  • 16
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    Oxford, UK : Blackwell Publishing Ltd
    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: The input to the described program, in learning mode, consists of examples of starting graph and result graph pairs. The starting graph is transformable into the result graph by adding or deleting certain edges and vertices. The essential common features of the starting graphs are stored together with specifications of the edges and vertices to be deleted or added. This latter information is obtained by mapping each starting graph onto the corresponding result graph. On subsequent input of similar starting graphs without a result graph, the program, in performance mode, recognizes the characterizing set of features in the starting graph and can perform the proper transformation on the starting graph to obtain the corresponding result graph. The program also adds the production to its source code so that after recompilation it is permanently endowed with the new production. If any feature which lacks the property “ordinary” is discovered in the starting graph and only one example has been given, then there is feedback to the user including a request for more examples to ascertain whether the extraordinary property is a necessary part of the situation.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: In this paper, we introduce and initiate a formalism to represent syntactic and semantic features in logic-based grammars. We also introduce technical devices to express feature-checking and feature-inheritance mechanisms. This leads us to propose some extensions to the basic unification mechanism of PROLOG. Finally, we consider the problem of long-distance dependency relations between constituents in gapping grammars rules from the point of view of morphosyntactic features that may change depending on the position occupied by the moved constituents. What we propose is not a new linguistic theory about features, but rather a formalism and a set of tools that we think will be useful to grammar writers to describe features and their relations in grammar rules.
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  • 18
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
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    Expert systems 3 (1986), S. 0 
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  • 20
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    Expert systems 3 (1986), S. 0 
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  • 21
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    Expert systems 3 (1986), S. 0 
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  • 22
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    Oxford, UK : Blackwell Publishing Ltd
    Expert systems 3 (1986), S. 0 
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  • 23
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Abstract: Fossil is an expert system for Palaeontology, written in Prolog. It consists of a knowledge base and three interfaces: a collector's ‘query’ interface; an expert's ‘update’ interface and a student's ‘review’ interface. As such, it covers the major uses of a knowledge base in palaeontology. The underlying model of expert system use and its supporting tools are described. This view is an alternative to that provioded by expert system shells of the Apes type. Such an approach has proved useful in Palaeontology and is likely to be applicable to other areas where the knowledge is arranged taxonomically. The use of Prolog as an implementation tool is briefly discussed.
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  • 24
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    Oxford, UK : Blackwell Publishing Ltd
    Expert systems 3 (1986), S. 0 
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
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    Topics: Computer Science
    Notes: Abstract: The use of knowledge engineering in diagnostic systems, is aimed primarily at exploiting procedural knowledge (about: systems operations, configuration, observations, calibration, maintenance), in connection with failure detection and test generation tasks. Next, the goal is to devise knowledge representation schemes whereby the failure events can be analyzed by merging highly diverse sources of information: analog/digital signals, logical variables and test outcomes, text from verbal reports, and inspection images. The final goal is to ease the operator workload when interfacing with the system under test and/or the test equipment, or with reliability assessment software packages. The paper will present key notions, methods and tools from: knowledge representation, inference procedures, pattern analysis. This will be illustrated by reference to a number of current and potential applications for e.g.: electronics failure detection, control systems testing, analysis of intermittent failures, false alarm reduction, test generation, maintenance trainers.
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  • 26
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    Oxford, UK : Blackwell Publishing Ltd
    Expert systems 3 (1986), S. 0 
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  • 27
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    Oxford, UK : Blackwell Publishing Ltd
    Expert systems 3 (1986), S. 0 
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  • 28
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Abstract: Evaluation of expert systems is an important step in the knowledge engineering process. In recent years, emphasis has been placed on knowledge acquisition, knowledge representation, and inferencing mechanisms. However, evaluation, and to a lesser extent, validation, have been slightly overlooked. This paper addresses some of the evaluation techniques that have been used for measuring information systems effectiveness and expert systems effectiveness. Specific attention is focused on the Analytic Hierarchy Process and Expert Choice. The evaluation results of an expert system prototype, called ‘Read’, are discussed via the use of the Analytic Hierarchy Process and Expert Choice.
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  • 29
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    Expert systems 3 (1986), S. 0 
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Abstract: This paper describes a conceptual framework for building expert systems in repair domains. A specific example of the use of this framework in building an expert system for a field service repair problem is given. The example system is designed to assist field service technicians in troubleshooting and repairing electronic systems at the board level. This system, a Field Service Advisor (Fieldserve), is designed (1) to diagnose single or multiple defects in electronic systems, (2) to guide a technician through appropriate repair procedures, (3) to verify diagnoses and monitor repair effectiveness and (4) to maintain records for subsequent evaluation and quality control.
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    Expert systems 3 (1986), S. 0 
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: We describe a shell for expert systems written in Prolog. The shell provides a consultation environment and a range of explanation capabilities. The design of the shell is modular, making it very easy to extend the shell with extra features required by a particular expert system. The novelty of the shell is twofold. Firstly, it has a uniform design consisting of an integrated collection of meta-interpreters. Secondly, there is a new approach for explaining ‘why not,’ when a query to the system fails.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Default reasoning is analyzed as consisting (implicitly) of at least three further aspects–oracles, jumps, and fixes-which in turn are related to the notion of a belief. Beliefs are then discussed in terms of their use in a reasoning agent. Next an idea of Israel is embellished to show that certain desiderata regarding these aspects of default reasoning lead to inconsistent belief sets, and that as a consequence the handling of inconsistencies must be taken as central to commonsense reasoning. Finally, these results are applied to standard cases of default reasoning formalisms in the literature (circumscription, default logic, and nonmonotonic logic), where it turns out that even weaker hypotheses lead to failure to achieve commonsense default conclusions.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: The primary goal of this paper is to illustrate how smaller deductive search spaces can be obtained by extending a logical language with restricted quantification and tailoring an inference system to this extension. The illustration examines the search spaces for a bottom-up parse of a sentence with a series of four strongly equivalent grammars. The grammars are stated in logical languages of increasing expressiveness, each restatement resulting in a more concise grammar and a smaller search space.A secondary goal is to point out an area where further research could yield results useful to the design of efficient parsers, particularly for grammatical formalisms that rely heavily on feature systems.
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    Computational intelligence 2 (1986), S. 0 
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    Topics: Computer Science
    Notes: Problem solvers that use heuristics to guide choices often run into untenable situations that can be characterized as overconstrained. When this happens, the problem must be able to identify the right culprit from among its heuristic choices in order to avoid a potentially explosive search. In this paper, we present a solution to this for a certain class of problems where the justifications associated with choice points involve an explicit assessment of the pros and cons of choosing each alternative relative to its competitors. We have designed a problem solver that accumulates such knowledge about the pros and cons of alternative selections at choice points during heuristic search, which it updates in light of an evolving problem situation. Whenever untenable situations arise, this preserved knowledge is used to determine the most appropriate backtracking point. By endowing the backtracker with access to this domain-specific knowledge, a highly contextual approach to reasoning in backtracking situations can be achieved.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
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    Topics: Computer Science
    Notes: Situation semantics proposes novel and attractive treatments for several problem areas of natural language semantics, such as efficiency (context sensitivity) and prepositional attitude reports. Its focus on the information carried by utterances makes the approach very promising for accounting for pragmatic phenomena. However, situation semantics seems to oppose several basic assumptions underlying current approaches to natural language processing and the design of intelligent systems in general. It claims that efficiency undermines the standard notions of logical form, entailment, and proof theory, and objects to the view that mental processes necessarily involve internal representations. The paper attempts to clarify these issues and discusses the impact of situation semantics’ criticisms for natural language processing, knowledge representation, and reasoning. I claim that the representational approach is the only currently practical one for the design of large intelligent systems, but argue that the representations used should be efficient in order to account for the system's embedding in its environment. The paper concludes by stating some constraints that a computational interpretation of situation semantics should obey and discussing remaining problems.
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    Computational intelligence 2 (1986), S. 0 
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Since Colmerauer's introduction of metamorphosis grammars (MGs), with their associated type-O-like grammar rules, there has been a desire to allow more general rule formats in logic grammars. Gap symbols were added to the MG rule by Pereira, resulting in extraposition grammars (XGs). Gaps, which are referenced by gap symbols, are sequences of zero or more unspecified symbols which may be present anywhere in a sentence or in a sentential form. However, XGs imposed restrictions on the position of gap symbols and on the contents of gaps. With the introduction of gapping grammars (GGs) by Dahl, these restrictions were removed but the rule was still required to possess a nonterminal symbol as the first symbol on the left-hand side. This restriction is removed with the introduction of unrestricted gapping grammars. FIGG, a flexible implementation of gapping grammars, possesses a bottom-up parser which can process a large subset of unrestricted gapping grammars. It can be used to examine the usefulness of unrestricted GGs for describing phenomena of natural languages such as free word order and partially free word/constituent order. Unrestricted gapping grammars, as implemented in FIGG, can also be used to describe grammars (or metagrammars) that utilize the gap concept, such as Gazdar's generalized phrase structure grammars.
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    Computational intelligence 2 (1986), S. 0 
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    Topics: Computer Science
    Notes: This paper reevaluates some of the contributions of Montague grammar in view of the increasing importance of computational considerations in linguistic theory and the demand for linguistic theories that can provide support in the design of natural language systems. It also considers Montague grammar in relation to work on lexical semantics and semantic nets. In this perspective the techniques of Montague grammar for systematically linking syntactic form and a model-theoretic semantics emerge as the most significant feature of the theory, while a number of the specific semantic assumptions recede in importance. Yet, with different ways of thinking about the structure mapping between levels of linguistic form and interpretations (e.g., constraint systems), we can also implement this connection using different techniques from what Montague had at his disposal.
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    Computational intelligence 2 (1986), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: Researchers developing and validating educational products often expect the same field-test activities to provide information on product improvement and product effectiveness. For effective and economical use of resources, these two goals, product improvement and product validation, must be stressed at different times and with different tools and strategies. This article identifies the difference in procedures and outcome between formative and summative evaluation practices and relates these practices to the development and validation of expert systems in education.
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    Notes: Most of the recent research on programming languages for education has been centered around the language Logo. In this paper we introduce another candidate language for learning environments, Nial, the nested interactive array language.Nial is a general-purpose programming language based on a formal theory of mathematics called array theory. This paper introduces Nial as a language for learning programming and developing and using computer-aided instruction tools. A comparison with Logo is provided to evaluate these two languages in terms of their strengths and weaknesses as programming environments for novice programmers. We also demonstrate that a programming environment can be both simple to leam at the novice level and extendible to a powerful and sophisticated language.
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    Topics: Computer Science
    Notes: This paper describes VP2, a system that has been implemented to tutor nonnative speakers in English. This system differs from many tutoring systems by employing an explicit grammar of its user's native language. This grammar enables VP2 to customize its responses by addressing problems due to interference of the native language. The system focuses on the acquisition of English verb-particle and verb-prepositional phrase constructions. Its correction strategy is based upon comparison of the native language grammar with an English grammar. VP2 is a modular system: its grammar of a user's native language can easily be replaced by a grammar of another language. The problems and solutions presented in this paper are related to the more general question of how modelling previous knowledge facilitates instruction in a new skill.
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    Topics: Computer Science
    Notes: ELECTRE is a project to build an intelligent tutoring system for learning basic electricity. This paper describes a student model based on the student's cognitive processes. This model includes, for each student, his/her domain knowledge and the specific heuristics. Moreover, it uses meta-knowledge of problem solving. This model is simulated by a knowledge-based system that controls the solving processes by meta-rules. A case study is presented.
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    Topics: Computer Science
    Notes: The focus of this paper is on the underlying knowledge base for an intelligent tutorial system for high-school algebra problems. We present a model of problem solving flexible enough to account for a variety of problem-solving behaviors and general enough to allow new problem domains to be defined easily. The model is based upon the analysis of protocols between students and expert tutors. We show how student errors can be monitored and remediated using the model, and we provide an approach to understanding problem difficulty that can be used to generate challenging problems and also provides a mechanism for planning their solution.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Computer Science
    Notes: This paper describes an object recognition algorithm both on a sequential machine and on a single instruction multiple data (SIMD) parallel processor such as the MIT connection machine. The problem, in the way it is presently formulated on a sequential machine, is essentially a propagation of constraints through a tree of possibilities in an attempt to prune the tree to a small number of leaves. The tree can become excessively large, however, and so implementations on massively parallel machines are sought in order to speed up the problem. Two fast parallel algorithms are described here, a static algorithm and a dynamic algorithm. The static algorithm reformulates the problem by assigning every leaf in the completely expanded unpruned tree to a separate processor in the connection machine. Then pruning is done in nearly constant time by broadcasting constraints to the entire SIMD array. This parallel version is shown to run three to four orders of magnitude faster than the sequential version. For large recognition problems which would exceed the capacity of the machine, a dynamic algorithm is described which performs a series of loading and pruning steps, dynamically allocating and deallocating processors through the use of the connection machine's global router communications mechanism.
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    Notes: We are concerned with developing a computational method for selecting possible antecedents of referring expressions over sentence boundaries. Our stratified model which uses a Λ-categorial language for meaning representation incorporates valuable features of Fregean-type semantics (a la Lewis, Montague, Partee, and others) along with features of situation semantics developed by Barwise and Perry. We consider a series of selected two-sentence stories which we use to illustrate referential interdependencies between sentences. We explain the conditions under which such dependencies arise, explain the conditions under which various translations can be performed, and formalize a set of rules which specify how to compute the reference. We restrict our discussion to two-sentence stories to avoid most of the problems inherent in where to look for the reference, that is, how to determine the proper antecedent. We restrict our considerations in this paper to situations where a reference, if it can be computed at all, has a unique antecedent. Thus we consider examples such as John wants to catch a fish. He (John) wants to eat it. and John interviewed a man. The man killed him (John). We then summarize the transformation which encompasses these rules and relate it to the stratified model. We discuss three aspects of this transformation that merit special attention from the computational viewpoint and summarize the contributions we have made. We also discuss the computational characteristics of the stratified model in general and present our ideas for a computer realization; there is no implementation of the t“ratified model at this time.
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    Computational intelligence 2 (1986), S. 0 
    ISSN: 1467-8640
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    Topics: Computer Science
    Notes: The SCENT (Student Computing ENvironmenT) project is concerned with building an intelligent tutoring system to help student programmers debug their LISP programs. The major thrust of current SCENT investigations is into the design of the SCENT advisor which is meant to provide debugging assistance to novice students. Six conceptual levels constitute the advisor. At the lowest level is the “raw data,” consisting of the student's (possibly buggy) program. This can be interpreted by a “program behaviour” level which can produce traces, cross-reference charts, etc. from the student's program. These traces, etc. can be analyzed by “observers” for interesting patterns. At the next level are “strategy judges” and “diagnosticians” which determine which strategy the student has used in his/her program and bugs in this strategy. A “task expert” provides task-specific input into the process of analyzing the student's solution, and a “student-knowledge component” provides student-specific input into this process. Information from the six levels interacts in a variety of ways and control is similarly hierarchical. This necessitates a blackboard-style scheme to coordinate information dissemination and control flow.This paper discusses the objectives of SCENT and focusses on organizing the process of debugging student programs. A complete example is given to illustrate how entities at the six levels interact and to indicate the kinds of information sharing that occur in the SCENT advisor. The paper concludes with an evaluation of the strengths and weaknesses of this approach to automated debugging, and suggestions about directions for further exploration.
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
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    Topics: Computer Science
    Notes: Abstract: AI technology is being used to develop expert systems that solve complex problems in the legal area. Most of these systems employ rules to describe the strategies and procedures used by litigators to analyze legal issues. The tasks performed by these systems include interpreting the law, anticipating the legal consequences of proposed actions, predicting the effects of changes in legislation, as well as analyzing and managing cases. The special characteristics of the legal domain cause certain problems for expert system builders. We discuss some of these problems and describe LDS and SAL, two expert systems we have developed for case evaluation and settlement in the product liability area. SAL (System for Asbestos Litigation) evolved from the earlier and more general expert system, LDS (Legal Decisionmaking System). We also describe XPL, an explanation facility we developed for use by SAL and other expert system applications.
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    Expert systems 3 (1986), S. 0 
    ISSN: 1468-0394
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    Notes: Abstract: This is a two part report. It looks at expert systems and the man–machine interface (mmi). We use the term mmi in a fairly broad sense. Specifically, we interpret the ‘man’ half of the interaction in two very different ways. Firstly, we look at man in terms of the ‘expert’ and consider the problem of how to get his or her knowledge into an expert system. Part One of the report therefore looks at what is currently happening in the area of knowledge acquisition in Britain and asks whether it really is the major bottleneck in the production of expert systems. Secondly, we look at man in terms of the ‘user’ and consider the best ways of making use of the knowledge once it is in an expert system. Part two of the report looks at cognitive aspects of the user interface, including dialogue control, explanation facilities, user models, natural language processing and the effects of new technology. It also considers the very important question of evaluation. Again we are concerned with what is actually happening in these areas in Britain today.
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    Expert systems 3 (1986), S. 0 
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    Expert systems 3 (1986), S. 0 
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    Notes: Abstract: Escort is a real time expert system which relieves the cognitive load on users of information systems generating large volumes of dynamic data. Escort is currently configured to help process plant operators in centralised control rooms. The system provides advice to the operators to help them handle and avoid crises. A demonstration system advising on a simulated oil production process has been implemented. Its key features are that it operates in real time, contains four domain knowledge bases, is controlled by a knowledge based scheduler and provides dynamic advice to the operator.
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    Notes: Abstract: Many expert systems have moved out of development laboratories into field test and routine use. About sixty such systems are listed. Academic research laboratories are contributing manpower to fuel the commercial development of AI. But the quantity of AI research may decline as a result unless the applied systems are experimented with and analyzed.
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    Mathematical programming 35 (1986), S. 110-119 
    ISSN: 1436-4646
    Keywords: Convex programming ; Frank-Wolfe algorithm
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    Topics: Computer Science , Mathematics
    Notes: Abstract We give a detailed proof, under slightly weaker conditions on the objective function, that a modified Frank-Wolfe algorithm based on Wolfe's ‘away step’ strategy can achieve geometric convergence, provided a strict complementarity assumption holds.
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    Mathematical programming 35 (1986), S. 125-125 
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    Mathematical programming 35 (1986), S. 140-172 
    ISSN: 1436-4646
    Keywords: Probabilistic analysis ; self-dual simplex ; spherical symmetry
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem ofn variables withm constraints. Smale established that for every number of constraintsm, there is a constantc(m) such that the number of pivot steps of the self-dual algorithm,ρ(m, n), is less thanc(m)(lnn) m(m+1) . We improve upon this estimate by showing thatρ(m, n) is bounded by a function ofm only. The symmetry of the function inm andn implies thatρ(m, n) is in fact bounded by a function of the smaller ofm andn.
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    Mathematical programming 35 (1986), S. 17-31 
    ISSN: 1436-4646
    Keywords: Linear complementarity problem ; K-matrix ; Q 0-matrix ; finite characterization ; Q-matrix
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    Topics: Computer Science , Mathematics
    Notes: Abstract The class of realn × n matricesM, known asK-matrices, for which the linear complementarity problemw − Mz = q, w ≥ 0, z ≥ 0, w T z =0 has a solution wheneverw − Mz =q, w ≥ 0, z ≥ 0 has a solution is characterized for dimensionsn 〈4. The characterization is finite and ‘practical’. Several necessary conditions, sufficient conditions, and counterexamples pertaining toK-matrices are also given. A finite characterization of completelyK-matrices (K-matrices all of whose principal submatrices are alsoK-matrices) is proved for dimensions 〈4.
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    Mathematical programming 34 (1986), S. 1-33 
    ISSN: 1436-4646
    Keywords: Polyhedra ; Chinese Postman ; Binary Group Problems ; Binary Matroids ; Blocking Clutters
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    Topics: Computer Science , Mathematics
    Notes: Abstract A new proof of the characterization of the Chinese postman polyhedra is given. In developing this proof, a theorem of Gomory about homomorphic lifting of facets for group polyhedra is generalized to subproblems. Some results for the Chinese postman problem are generalized to binary group problems. In addition, a connection is made between Fulkerson's blocking polyhedra and a blocking pair of binary group problems. A connection is also developed between minors and lifting of facets for group problems.
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    Mathematical programming 34 (1986), S. 48-61 
    ISSN: 1436-4646
    Keywords: Total Dual Integrality ; Hilbert Basis ; Polyhedra
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    Topics: Computer Science , Mathematics
    Notes: Abstract Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra. In this paper a geometric characterization of these polyhedra is given. This geometric result is used to show that each TDI defining system for a box TDI polyhedron is in fact a box TDI system, that the class of box TDI polyhedra is in co-NP and is closed under taking projections and dominants, that the class of box perfect graphs is in co-NP, and a result of Edmonds and Giles which is related to the facets of box TDI polyhdera.
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    Mathematical programming 34 (1986), S. 72-83 
    ISSN: 1436-4646
    Keywords: Cutting Planes ; Disjunctive Programming
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    Notes: Abstract The duality between facets of the convex hull of disjunctive sets and the extreme points of reverse polars of these sets is utilized to establish simple rules for the derivation of all facet cuts for simple disjunctions, namely, elementary disjunctions in nonnegative variables. These rules generalize the cut generation procedure underlying polyhedral convexity cuts with negative edge extensions. The latter are also shown to possess some interesting properties with respect to a biextremal problem that maximizes the distance, from the origin, of the nearest point feasible to the cut. A computationally inexpensive procedure is given to generate facet cuts for simple disjunctions which are dominant with respect to any specified preemptive ordering of variables.
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    Mathematical programming 34 (1986), S. 111-124 
    ISSN: 1436-4646
    Keywords: Global Optimization ; Stochastic Optimization ; Annealing ; Metropolis Method ; NP ; Hill Climbing ; Local Improvement
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    Notes: Abstract The annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems, including NP-hard combinatorial problems such as the travelling salesman, Steiner trees and others. There is an appealing physical analogy for its operation, but a more formal model seems desirable. In this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1. We also show that there are cases where convergence takes exponentially long—that is, it is no better than a deterministic method. We study how the convergence rate is affected by the form of the problem. Finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of ‘practical’ confidence in the solution.
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    Mathematical programming 34 (1986), S. 125-141 
    ISSN: 1436-4646
    Keywords: Assignment Problem ; Dual Method ; Signature ; Linear Programming ; Simplex Method ; Pivoting ; Average Behavior
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract “Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling.” - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974). A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx ij 〈 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx ij is shown to converge in at most ( 2 n-1 ) pivots, and at most O(n 3) time, and it is argued that on average the number of pivots is at mostn logn.
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    Mathematical programming 34 (1986), S. 142-162 
    ISSN: 1436-4646
    Keywords: Network Design ; Bilevel Programming ; Variational Inequalities ; Stackelberg Games
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    Topics: Computer Science , Mathematics
    Notes: Abstract Recently much attention has been focused on multilevel programming, a branch of mathematical programming that can be viewed either as a generalization of min-max problems or as a particular class of Stackelberg games with continuous variables. The network design problem with continuous decision variables representing link capacities can be cast into such a framework. We first give a formal description of the problem and then develop various suboptimal procedures to solve it. Worst-case behaviour results concerning the heuristics, as well as numerical results on a small network, are presented.
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    Mathematical programming 34 (1986), S. 175-187 
    ISSN: 1436-4646
    Keywords: Primary 65K05 ; Secondary 90C25 ; Nonsmooth Optimization ; Nondifferentiable Programming ; Linearly Constrained Minimization ; Descent Methods
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    Topics: Computer Science , Mathematics
    Notes: Abstract A readily implementable algorithm is given for minimizing a (possibly nondifferentiable and nonconvex) locally Lipschitz continuous functionf subject to linear constraints. At each iteration a polyhedral approximation tof is constructed from a few previously computed subgradients and an aggregate subgradient, which accumulates the past subgradient information. This aproximation and the linear constraints generate constraints in the search direction finding subproblem that is a quadratic programming problem. Then a stepsize is found by an approximate line search. All the algorithm's accumulation points are stationary. Moreover, the algorithm converges whenf happens to be convex.
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    Mathematical programming 34 (1986), S. 248-249 
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    Mathematical programming 34 (1986), S. 251-264 
    ISSN: 1436-4646
    Keywords: Integer Linear Programming ; Chvátal Rank ; Cutting Planes ; Sensitivity Analysis
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    Topics: Computer Science , Mathematics
    Notes: Abstract We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax≤b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixA. Using this, we strengthen several integer programming ‘proximity’ results of Blair and Jeroslow; Graver; and Wolsey. We also show that the Chvátal rank of a polyhedron {x: Ax≤b} can be bounded above by a function of the matrixA, independent of the vectorb, a result which, as Blair observed, is equivalent to Blair and Jeroslow's theorem that ‘each integer programming value function is a Gomory function.’
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    Mathematical programming 34 (1986), S. 302-332 
    ISSN: 1436-4646
    Keywords: Generalized Programming ; Competitive Equilibria ; Economic Modelling
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    Topics: Computer Science , Mathematics
    Notes: Abstract We present a modification of the Manne-Chao-Wilson algorithm for computing competitive equilibria and discuss some of its convergence properties. Numerical experiments involving models with up to 100 price responsive agents are provided.
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    Mathematical programming 34 (1986), S. 292-301 
    ISSN: 1436-4646
    Keywords: Selection Rules ; Linear Programming ; Linear Complementarity ; Network Flows
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    Notes: Abstract Affirmative action is a new variety of selection rule which employs historical information to favor the choice of elements that have not been selected in the past. We categorize three implementations of this principle and discuss their application to the simplex method, to Bard-type schemes for the linear complementarity problem, and to augmenting path methods for network flow problems. We present analytical and computational results, and some open questions.
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    Mathematical programming 34 (1986), S. 265-291 
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    Keywords: Linear Complementarity Problems ; Complementary Cones ; Invariant Number of Solutions
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    Notes: Abstract This paper studies the class INS of all realn × n matricesM for which the linear complementarity problem (q, M) has exactlyk solutions—k depending only onM—for all realn-vectorsq interior to the coneK(M) of vectors for which (q, M) has any solution at all. This generalizes the results in Cottle and Stone (1983) which deal with the subclassU in INS wherek equals one. After the first two sections of this paper, which introduce the problem and background material, we move on to examine necessary conditions for a matrixM to be in INS (Section 3) and sufficient conditions under whichM will be in INS (Section 4). Section 5 deals with the possible values whichk may have. Section 6 discusses related results concerning the geometry of linear complementarity problems. Finally, Section 7 deals with some known and new matrix classes which are in INS.
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    Mathematical programming 34 (1986), S. 370-371 
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    Mathematical programming 34 (1986), S. 372-372 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Bestimmung von Iterierten hoher Ordnung von Abbildungen in der Nähe der Identität ist ein wichtiges Problem in der Theorie nichtlinearer Schwingungen. Unter Verwendung von Methoden aus der Asymptotischen Analysis wird eine effiziente Extrapolationsmethode abgeleitet und angewendet, insbesondere auf die sogenannten Lorenz-Gleichungen.
    Notes: Abstract The determination of high order iterates of near identity maps is a problem of considerable interest in the theory of non-linear oscillations. Using tools from Asymptotic Analysis we derive an efficient extrapolation method and apply it in various situations, and in particular to the Lorenz equations.
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    Computing 37 (1986), S. 31-42 
    ISSN: 1436-5057
    Keywords: Primary 65D32 ; secondary 65R20 ; Cauchy principal value integral ; singular integral equations ; quadrature rules ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit konstruieren wir eine interpolatorische Quadraturformel der Form $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 \frac{{f'(x)}}{{y - x}}dx \approx \sum\limits_{i = 1}^n {w_{ni} (y)f(x_{ni} )} ,$$ wobeif(x)=(1−x)α(1+x)β f 0(x), α, β〉0, und {xni} dien Nullstellen des Chebyshevpolynomsn-ten Grades vom ersten TypT n (x) sind. Ferner geben wir ein Konvergenzergebnis an und untersuchen das Verhalten der Größe $$ \sum\limits_{i = 1}^n {|w_{ni} (y)|} $$ , fürn→∞.
    Notes: Abstract In this paper we construct an interpolatory quadrature formula of the type $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 \frac{{f'(x)}}{{y - x}}dx \approx \sum\limits_{i = 1}^n {w_{ni} (y)f(x_{ni} )} ,$$ wheref(x)=(1−x)α(1+x)β f o(x), α, β〉0, and {x ni} are then zeros of then-th degree Chebyshev polynomial of the first kind,T n (x). We also give a convergence result and examine the behavior of the quantity $$ \sum\limits_{i = 1}^n {|w_{ni} (y)|} $$ asn→∞.
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    Computing 37 (1986), S. 93-102 
    ISSN: 1436-5057
    Keywords: 68NO5 ; 68Q25 ; Towers of Hanoi ; performance evaluation ; algorithm ; iteration ; recursion ; binary number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird ein Satz über die Bezihung zwischen den Türmen von Hanoi und den Binärzahlen bewiesen. Aus diesem Satz folgt ein Algorithmus für das Problem der Türme von Hanoi. Die Komplexitätsabschätzungen aller existierenden rekursiven und iterativen Algorithmen für das Problem der Türme von Hanoi zeigen, daß der angegebene iterative Algorithmus der effizienteste in Bezug auf Laufzeit und Speicherplatz ist. Schließlich wird gezeigt, daß die Binärdarstellung von Zahlen den Status allern-Scheiben in jedem Schritt vollständig charakterisiert.
    Notes: Abstract A theorem concerning the relation between the Towers of Hanoi and the binary numbers is proven in this paper. From this theorem, an algorithm for the Towers of Hanoi problem follows. The performance evaluations of all existing recursive and iteative algorithms for the Towers of Hanoi problem show that the above iterative algorithm is the most efficient one in terms of time and space. Finally, it is shown that the binary representation of numbers completely characterizes the status of alln discs in each step.
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    ISSN: 1436-5057
    Keywords: 65N30 ; 65H10 ; Nonlinear radiation cooling problem ; finite element solution ; explicit monotone iterations ; upper and lower bounds
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit beobachten wir das explizite monotone Iterationsverfahren von finiten Elementlösungen für das Radiationskühlungsproblem mit nichtlinearen Randbedingungen. Bei diesem Iterationsverfahren ergeben sich obere und untere Schranken, und eine Konvergenz kann nachgewiesen werden. An einigen numerischen Beispielen wird die Brauchbarkeit gezeigt.
    Notes: Abstract In this paper we consider explicit monotone iterations of the finite element solutions for the radiation cooling problem with the nonlinear boundary conditions. These iterations provide upper and lower bounds, and convergence proofs are given. Finally, we give some numerical examples to demonstrate the effectiveness.
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    Keywords: 90C30 ; 65K05 ; Nonlinear programming algorithms ; hybrid algorithms
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    Description / Table of Contents: Zusammenfassung Zur Bestimmung von Kuhn-Tucker-Punkten nichtlinearer Optimierungsaufgaben wird ein hybrides numerisches Verfahren vorgestellt. Ausgangspunkt der Betrachtungen sind die in diesem Journal erschienenen Arbeiten von Best/Bräuninger/Ritter/Robinson und Kleinmichel/ Richter/Schönefeld, in denen verschiedene lokal überlinear konvergente Verfahren mit einer Strafmethode kombiniert werden, so daß sich für die so entstehenden Verfahren auch die globale Konvergenz nachweisen läßt. Als Beispiel dafür, daß das zugrunde liegende Kopplungsprinzip auf eine Reihe weiterer global konvergenter Verfahren angewendet werden kann, wird ein lokales Verfahren vom Wilson-Typ initialisiert durch ein Verfahren der zulässigen Richtungen, welches unter Benutzung reduzierter Gradienten arbeitet. In beiden Phasen des Verfahrens treten gleichartige Ersatzprobleme in Form spezieller quadratischer Optimierungsaufgaben auf. Daher sind im Gegensatz zu den oben angeführten Arbeiten ausschließlich lineare Gleichungssysteme zu lösen. Unter den üblichen Voraussetzungen läßt sich für das Gesamtverfahren die globale und lokal überlineare Konvergenz zeigen.
    Notes: Abstract For solving nonlinear optimization problems, i.e. for the determination of Kuhn-Tucker points a numerical method is proposed. The considerations continue investigations of Best/ Bräuninger/Ritter/Robinson and Kleinmichel/Richter/Schönefeld. In these papers (published in this journal) different local methods are combined with a penalty method in such a way that global convergence can be guaranteed. In order to show that the basic principle of coupling is applicable to a number of further globally convergent methods a local Wilson-type method is now initialized by a feasible direction method that uses reduced gradients. In both phases of the method similar subproblems (special quadratic programs) occur. Therefore, in contrast to the papers mentioned above systems of linear equations have to be solved exclusively. Under usual assumptions the algorithm is shown to be globally and superlinearly convergent.
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  • 80
    ISSN: 1436-5057
    Keywords: 65L05 ; G.1.7 ; G.1.8 ; Numerical analysis ; ordinary differential equations ; Runge-Kutta methods ; predictorcorrector methods ; periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für die numerische Behandlung von Differentialgleichungen zweiter Ordnung, bei dennen die Lösung im wesentlichen durch die von einer äußeren periodischen Kraft erzwungenen Schwingung bestimmt wird, werden Diskretisierungsmethoden vom Runge-Kutta-Nyström Typ und spezielle Prädiktor-Korrektor Methoden konstruiert. Für eine Klasse expliziter und linear-impliziter Runge-Kutta-Nyström Methoden der Ordung zwei zeigen wir, daß die erzwungene Schwingung keinen Phasenfehler aufweist. Für eine Klasse von Prädiktor-Korrektor Methoden vierter Ordnung wird nachgewiesen, daß die Phasen- und Dissipationsfehlerordnung beliebig groß gemacht werden kann. Numerische Beispiele bestätigen die Wirksamkeit unserer Methoden mit reduziertem Phasenfehler.
    Notes: Abstract Runge-Kutta-Nyström type methods and special predictor-corrector methods are constructed for the accurate solution of second-order differential equations of which the solution is dominated by the forced oscillation originating from an external, periodic forcing term. For a family of second-order explicit and linearly implicit Runge-Kutta-Nyström methods it is shown that the forced oscillation is represented with zero phase lag. For a family of predictor-corrector methods of fourth-order, it is shown that both the phase lag order and the dissipation of the forced oscillation can be made arbitrarily high. Numerical examples illustrate the effectiveness of our reduced phase lag methods.
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    Computing 37 (1986), S. 255-259 
    ISSN: 1436-5057
    Keywords: 65 G 10 ; 65 H 05 ; 65 F 30 ; Order of convergence ; interval methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten hier eine Klasse von Rekursionsfolgen, die eine Verallgemeinerung von den in [3] behandelten ist. Dazu werden Abschätzungen für dieR-Ordnung hergeleitet und dann auf eine Klasse von Iterationsverfahren zur Einschließung der Inversen einer Matrix angewendet.
    Notes: Abstract In this note we are considering a class of recurrences which is a generalization of those in [3]. Estimates for theirR-order are derived and the results are then applied to a family of higher-order interval methods for the inclusion of the inverse of a matrix. An efficient algorithm is determined.
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    Computing 37 (1986), S. 277-301 
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    Description / Table of Contents: Zusammenfassung Wir geben einen möglichst vollständigen Überblick über alle gebräuchlichen Prüfziffern-Verfahren. Der gruppentheoretische Hintergrund aller dieser Verfahren wird erklärt, und es wird gezeigt, wie sich auf dieser Basis neue Prüfzeichen-Verfahren konstruieren lassen. Mit Hilfe lateinischer Quadrate (oder Quasigruppen) werden neue Prüfzeichen-Verfahren gefunden, speziell ein guter dezimaler Shift-Code.
    Notes: Abstract A hopefully complete review is given of different decimal codes that are in use. The grouptheoretical background of those methods is explained and applied to the construction of new error detecting codes. With the help of Latin squares (or quasi-groups) new error codes are found, especially a good decimal shift-code.
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  • 83
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    Computing 37 (1986), S. 351-355 
    ISSN: 1436-5057
    Keywords: 65F10 ; Matrix equation ; algebraic formula
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    Description / Table of Contents: Zusammenfassung Angegeben wird eine algebraische Formel für die Lösung der GleichungAX−XB=C und ein auf ihr basierender Lösungsalgorithmus.
    Notes: Abstract In this paper a finite algebraic formula for the solution of the matrix equationAX−XB=C is derived. Based on it, a new direct algorithm is given.
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  • 84
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    Computing 37 (1986), S. 357-364 
    ISSN: 1436-5057
    Keywords: (1970) Primary 65D30 ; Analytic function ; double integral ; approximation ; degree of precision
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine 9punktige Formel vom Grad 5 zur numerischen Approximation von Doppelintegralen komplexer Variablen samt Fehlerschranke hergeleitet.
    Notes: Abstract A nine-point degree five rule for the numerical approximation of double integrals of analytic functions of complex variables and its error bound have been derived.
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  • 85
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    Computing 37 (1986), S. 365-370 
    ISSN: 1436-5057
    Keywords: Maximal minimally strongly connected (MMSC) subgraphs ; cliques ; performance ; complexities ; cluster analysis ; maximal compatibles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In einer kürzlich erfolgten Veröffentlichung von Daset al. wurde ein Algorithmus zur Erzeugung maximaler minimal stark zusammenhängender (MMSC) Untergraphen oder Cliquen in ungerichteten Graphen vorgeschlagen. Dieser Algorithmus basiert auf einer Verfeinerung der Technik der sukzessiven Aufspaltung, der von Paull und Unger eingeführt wurde. In der vorliegenden Arbeit wird das Leistungsverhalten dieses Algorithmus bei Implementierung in FORTRAN IV mit dem System Cyber 170/720 untersucht.
    Notes: Abstract An algorithm for generating maximal minimally strongly connected (MMSC) subgraphs or cliques in undirected graphs has been suggested by Daset al. in a recent paper. The proposed algorithm is based on a refinement of the technique of successive splitting described by Paull and Unger in the determination of maximal compatibles of states in the context of minimization of incomplete sequential machines. The present paper discusses the performance of the aforementioned subgraph generation algorithm in an implementation on Cyber System 170/720 using FORTRAN IV, in particular reference to cluster analysis.
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  • 86
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    Engineering with computers 1 (1986), S. 127-147 
    ISSN: 1435-5663
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract One of the major problems in developing computeraided design software is the establishment of effective man-machine communication. This paper describes a computer-aided plate girder design software package and its man-machine interface using natural language processing techniques. The natural language interpreter takes advantage of the user's communication and technical skills and accepts commands in the user's native language. The user can verify the correct interpretation of the commands from the responsive graphic display of the design.
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  • 87
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    Engineering with computers 1 (1986), S. 175-191 
    ISSN: 1435-5663
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract With the aid of the supercomputer we have performed three-dimensional simulations in practical cpu time. At the same time, though, huge amounts of output data must be treated automatically by post processors, so that only necessary information will be extracted and changes of models, mesh subdivisions, or boundary conditions will be taken into account. This type of information processing cannot be attained by conventional postprocessors, and a new concept of postprocessing and system must be developed in the sense of computer-aided engineering or computer diagnosis. We present a computer tomographic system COMTOS-BEM based on three-dimensional boundary element analysis; it houses its own geometric modeling and automatic mesh generation. Furthermore, it supports design feedback reactions to change modeling or meshing, make recalculations, and renew boundary conditions. In this paper, we state the basic concept of the proposed computer diagnosis system and present the necessary geometric modeling and processing and boundary element formulations. Some numerical examples illustrate the validity and effectiveness of our system in practice.
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  • 88
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    Engineering with computers 1 (1986), S. 205-215 
    ISSN: 1435-5663
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A computerized procedure for symbolic manipulations and FORTRAN code generation of elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, the Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.
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  • 89
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    Mathematical programming 34 (1986), S. 188-200 
    ISSN: 1436-4646
    Keywords: Global Maximum
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    Topics: Computer Science , Mathematics
    Notes: Abstract This algorithm for global optimization uses an arbitrary starting point, requires no derivatives, uses comparatively few function evaluations and is not side-tracked by nearby relative optima. The algorithm builds a gradually closer piecewise-differentiable approximation to the objective function. The computer program exhibits a (theoretically expected) strong tendency to cluster around relative optima close to the global. Results of testing with several standard functions are given.
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  • 90
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    Mathematical programming 34 (1986), S. 163-174 
    ISSN: 1436-4646
    Keywords: Global Minimization ; Separable Programming ; Quadratic Programming ; Large-Scale
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    Topics: Computer Science , Mathematics
    Notes: Abstract The global minimization of a large-scale linearly constrained concave quadratic problem is considered. The concave quadratic part of the objective function is given in terms of the nonlinear variablesx ∈R n , while the linear part is in terms ofy ∈R k. For large-scale problems we may havek much larger thann. The original problem is reduced to an equivalent separable problem by solving a multiple-cost-row linear program with 2n cost rows. The solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum, and also gives a bound on the relative error in the function value of this incumbent. Ana priori bound on this relative error is obtained, which is shown to be ≤ 0.25, in important cases. If the incumbent is not a satisfactory approximation to the global minimum, a guaranteedε-approximate solution is obtained by solving a single liner zero–one mixed integer programming problem. This integer problem is formulated by a simple piecewise-linear underestimation of the separable problem.
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    Mathematical programming 34 (1986), S. 201-211 
    ISSN: 1436-4646
    Keywords: Stability ; Invariant Capital Stocks—Boundary Type and Interior Type ; Critical Discount Factor
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study the stability of two types of Invariant Capital Stocks which are shown to exist in a two-dimensional planning model. It is shown that, for each type of Invariant Capital Stock, there is a critical discount factor such that when the discount factor falls below it, the corresponding Invariant Capital Stock will become unstable.
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    Mathematical programming 34 (1986), S. 232-234 
    ISSN: 1436-4646
    Keywords: Convex-Concave Like Functions ; Fan's Minimax Theorem ; Separation Theorem
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    Topics: Computer Science , Mathematics
    Notes: Abstract A new brief proof of Fan's minimax theorem for convex-concave like functions is established using separation arguments.
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  • 93
    ISSN: 1436-4646
    Keywords: Boolean Inequalities ; Implication Graph ; Depth-First Search ; Strongly Connected Components ; Transitive Closure ; 0–1 Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a setR ofm binary relations on a set ofn boolean variables.R may imply a contradiction, the fixation of some variables at 0 or at 1 and/or the identification of some pairs of variables in direct or complemented form. An O(n) expected-time algorithm is given for the derivation of all such logical conclusions. Computational experiments with problems involving up to 2000 variables are reported on. The proposed algorithm is more than 100 times faster than previous methods whenn ≥ 100.
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    Mathematical programming 34 (1986), S. 235-238 
    ISSN: 1436-4646
    Keywords: Linear Programming ; Characterization of Optimality ; Dual Program
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    Notes: Abstract We present a characterization of the ‘normal’ optimal solution of the linear program given in canonical form max{c tx: Ax = b, x ≥ 0}. (P) We show thatx * is the optimal solution of (P), of minimal norm, if and only if there exists anR 〉 0 such that, for eachr ≥ R, we havex * = (rc − Atλr)+. Thus, we can findx * by solving the following equation forλ r A(rc − Atλr)+ = b. Moreover,(1/r)λ r then ‘converges’ to a solution of the dual program.
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  • 95
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    Mathematical programming 34 (1986), S. 212-222 
    ISSN: 1436-4646
    Keywords: Linear Production ; Cooperative Games ; Core of a Game ; Linear Programming ; Network Optimization ; Spanning Tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producersS is not restricted to be the vector sum of the resources held by the members ofS. We provide sufficient conditions for the non-emptiness of the core of the associated generalized linear production game, and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem. Our generalized linear production model is a proper generalization of the linear production model introduced by Owen, and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework. We use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non-empty core. We further employ our model to prove the non-emptiness of the core of two other classes of cooperative games, which were not previously studied in the literature, and we also use our generalized model to provide an alternative proof for the non-emptiness of the core of the class of minimum cost spanning tree games. Thus, it appears that the generalized linear production model is a unifying model which can be used to explain the non-emptiness of the core of cooperative games generated by various, seemingly different, optimization models.
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    Mathematical programming 34 (1986), S. 239-242 
    ISSN: 1436-4646
    Keywords: Complementarity ; Lemke's Algorithm
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    Topics: Computer Science , Mathematics
    Notes: Abstract This note presents a new termination result for the Lemke linear complementarity algorithm that unifies two previous results. Special cases include linear complementarity problems satisfying the Evers condition, and those whoseM matrix is copositive-plus.
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    Mathematical programming 34 (1986), S. 243-247 
    ISSN: 1436-4646
    Keywords: Stochastic Games ; Undiscounted Rewards ; Stationary Strategies ; Nonlinear Programming
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    Topics: Computer Science , Mathematics
    Notes: Abstract We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.
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    Mathematical programming 34 (1986), S. 250-250 
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    Mathematical programming 34 (1986), S. 373-373 
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    Computing 36 (1986), S. 335-342 
    ISSN: 1436-5057
    Keywords: 65D07 ; 41A15 ; 90C20 ; Convexity conditions ; weakly coupled system of inequalities ; numerical algorithms ; quadratic programming ; unconstrained dual program with tridiagonal Hessian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Während die Aufgabe der konvexen Interpolation im Falle kubischer Splines im allgemeineen nicht lösbar ist, kann jetzt gezeigt werden, daß sie bei Verwendung von Exponentialsplines Lösungen besitzt sofern die vorkommenden Parameter hinreichend roß sind, und es werden konkrete hinreichende und notwendige Lösbarkeitsbedingungen hergeleitet. Da eindeutige Lösbarkeit in der Regel nicht vorliegt, wird eine Auswahlfunktion eingeführt und das entstehende quadratische Optimierungsproblem nach Dualisierung numerisch behandelt.
    Notes: Abstract Sufficient and necessary conditions are derived under which interpolating splines are convex if the data set is in convex position. In order to select one of the interpolants, by means of a well-known objective function a quadratic optimization problem is stated which can be solved effectively by passing to a dual program.
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