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  • Articles  (57,317)
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  • 1
    Electronic Resource
    Electronic Resource
    An asynchronous parallel newton method (1988)
    Springer
    Mathematical programming 42 (1988), S. 363-374 
    Details
    ISSN: 1436-4646
    Keywords: Newton method ; parallel algorithms ; superlinear convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A parallel Newton method is described for the minimization of a twice continuously differentiable uniformly convex functionF(x). The algorithm generates a sequence {x j } which converges superlinearly to the global minimizer ofF(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589411
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  • 2
    Electronic Resource
    Electronic Resource
    Generalized polymatroids and submodular flows (1988)
    Springer
    Mathematical programming 42 (1988), S. 489-563 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Polyhedra related to matroids and sub- or supermodular functions play a central role in combinatorial optimization. The purpose of this paper is to present a unified treatment of the subject. The structure of generalized polymatroids and submodular flow systems is discussed in detail along with their close interrelation. In addition to providing several applications, we summarize many known results within this general framework.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589418
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  • 3
    Electronic Resource
    Electronic Resource
    S3 sets. An extension of the Beale-Tomlin special ordered sets (1988)
    Springer
    Mathematical programming 42 (1988), S. 113-123 
    Details
    ISSN: 1436-4646
    Keywords: Scheduling ; large-scale 0–1 model ; variable fixing ; coefficient reduction ; special ordered sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this work an extension of the Beale-Tomlin special ordered sets is introduced that has proved to be efficient for solving certain types of open shop scheduling problems. Besides their usual characteristics, exclusivity constraints in the jobs are allowed, more general than tree-like precedence structures are considered, and semi-active schedules that cannot be labeled as non-optimal solutions may occur. The problem is formulated as a large-scale 0–1 model. Computational experience on some real-life problems is reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589396
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  • 4
    Electronic Resource
    Electronic Resource
    Impacs - A bus crew scheduling system using integer programming (1988)
    Springer
    Mathematical programming 42 (1988), S. 181-187 
    Details
    ISSN: 1436-4646
    Keywords: Branch and bound ; bus crew scheduling ; integer programming ; scheduling ; set covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589402
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  • 5
    Electronic Resource
    Electronic Resource
    Dual coordinate step methods for linear network flow problems (1988)
    Springer
    Mathematical programming 42 (1988), S. 203-243 
    Details
    ISSN: 1436-4646
    Keywords: Network flows ; relaxation ; distributed algorithms ; complexity ; asynchronous algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion ofε-complementary slackness, and most do not explicitly manipulate any “global” objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of newserial computational complexity results. We develop the basic theory of these methods and present two specific methods, theε-relaxation algorithm for the minimum-cost flow problem, and theauction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 logNC) and O(NA logNC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implementε-relaxation in a completely asynchronous, “chaotic” environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589405
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  • 6
    Electronic Resource
    Electronic Resource
    Parallel application of block-iterative methods in medical imaging and radiation therapy (1988)
    Springer
    Mathematical programming 42 (1988), S. 307-325 
    Details
    ISSN: 1436-4646
    Keywords: Full discretization ; computerized tomography ; image reconstruction ; radiotherapy treatment planning ; block-iterative algorithms ; parallel computations ; Cimmino's algorithm ; entropy maximization ; classification of algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Some row-action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems. Recently developed block-iterative versions of such special-purpose methods enable parallel computation when the underlying problem is appropriately decomposed. This opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning, all in their fully discretized modelling approach. Since there is more than one way of deriving block-iterative versions of any row-action method, the choice has to be made with reference to the underlying real-world problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589408
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  • 7
    Electronic Resource
    Electronic Resource
    Decomposition of linear programs using parallel computation (1988)
    Springer
    Mathematical programming 42 (1988), S. 391-405 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; large-scale-systems ; decomposition ; parallel computing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes DECOMPAR: an implementation of the Dantzig-Wolfe decomposition algorithm for block-angular linear programs using parallel processing of the subproblems. The software is based on a robust experimental code for LP decomposition and runs on the CRYSTAL multicomputer at the University of Wisconsin-Madison. Initial computational experience is reported. Promising directions in future development of this approach are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589413
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  • 8
    Electronic Resource
    Electronic Resource
    A matroid algorithm and its application to the efficient solution of two optimization problems on graphs (1988)
    Springer
    Mathematical programming 42 (1988), S. 471-487 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We address the problem of finding a minimum weight baseB of a matroid when, in addition, each element of the matroid is colored with one ofm colors and there are upper and lower bound restrictions on the number of elements ofB with colori, fori = 1, 2,⋯,m. This problem is a special case of matroid intersection. We present an algorithm that exploits the special structure, and we apply it to two optimization problems on graphs. When applied to the weighted bipartite matching problem, our algorithm has complexity O(|E∥V|+|V| 2log|V|). HereV denotes the node set of the underlying bipartite graph, andE denotes its edge set. The second application is defined on a general connected graphG = (V,E) whose edges have a weight and a color. One seeks a minimum weight spanning tree with upper and lower bound restrictions on the number of edges with colori in the tree, for eachi. Our algorithm for this problem has complexity O(|E∥V|+m 2 |V|+ m|V| 2). A special case of this constrained spanning tree problem occurs whenV * is a set of pairwise nonadjacent nodes ofG. One must find a minimum weight spanning tree with upper and lower bound restrictions on the degree of each node ofV *. Then the complexity of our algorithm is O(|V∥E|+|V * ∥V| 2). Finally, we discuss a new relaxation of the traveling salesman problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589417
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  • 9
    Electronic Resource
    Electronic Resource
    A new kind of combinations between the Ritz-Galerkin and finite element methods for singularity problems (1988)
    Springer
    Computing 40 (1988), S. 29-50 
    Details
    ISSN: 1436-5057
    Keywords: Primary 65N10 ; 65N30 ; Elliptic problems ; singularity problems ; finite element methods ; Ritz-Galerkin methods ; combined methods ; nonconforming combinations ; penalty combined methods ; simplified hybridcombined methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Koppelungstechniken zwischen der Ritz-Galerkin- und der Lagrange-Finite-Elemente-Methode der Ordnungk≥1 vorgestellt, die aus einer Kombination von hybriden Techniken und Straffunktionstechniken bestehen. Mit ihrer Hilfe werden komplizierte Probleme bei homogenen und inhomogenen elliptischen Gleichungen gelöst, insbesondere mit Singularitäten oder auf unbeschränkten Bereichen. Für die numerischen Lösungen werden optimale Konvergenzraten in Sobolev-Normen bewiesen. Diese theoretischen Ergebnisse werden in numerischen Experimenten für die singuläre Motz-Gleichung verifiziert.
    Notes: Abstract The coupling techniques of simplified hybrid plus penalty functions are first presented for matching the Ritz-Galerkin method and thek(k〉-1)-order Lagrange finite element methods to solve complicated problems of elliptic equations, homogeneous or nonhomogeneous, in particular with singularities or unbounded domains. Optimal convergence rates of numerical solutions have been proved in the Sobolev norms. Moreover, the theoretical results obtained in this paper have been verified by numerical experiments for the singular Motz problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242188
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  • 10
    Electronic Resource
    Electronic Resource
    Bit serial addition trees and their applications (1988)
    Springer
    Computing 40 (1988), S. 9-17 
    Details
    ISSN: 1436-5057
    Keywords: B.5.1 [Register-Transfer-Level Implementation] Design-Arithmetic and logic units ; B.6.1 [Logic Design]: Design styles-Parallel circuits ; F.2.0. [Analysis of Algorithms and Problem Complexity]: General ; Algorithms ; Parallel algorithm ; logical circuit ; binary integer ; bit serial ; addition ; multiplication ; matrix multiplication ; selection ; sorting ; statistical computations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir untersuchen parallele Algorithmen für eine Anzahl von grundlegenden Rechenproblemen. Alle Algorithmen besitzen als Grundoperation die Additionk-stelliger Binärzahlen. Für jedes Problem geben wir die Lösung in Form eines logischen Schaltkreises, für den das Produkt aus Rechenzeit und Anzahl der benutzten Gatter kleiner ist als bei den besten bisher bekannten Algorithmen.
    Notes: Abstract Parallel algorithms are examined for a number of fundamental computational problems. All algorithms have as a basic operation the addition ofk-bit integers. For each problem we present a solution in the form of a logical circuit for which the product of the computation time and number of gates used is smaller than that of the best previously known algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242186
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