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  • Articles  (13)
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  • global optimization  (13)
  • Springer  (13)
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  • Articles  (13)
  • Other Sources
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  • Springer  (13)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
  • Annual Reviews
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  • 2000-2004
  • 1995-1999  (13)
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  • 1
    Electronic Resource
    Electronic Resource
    Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 487-510 
    Details
    ISSN: 1573-2878
    Keywords: Multiplicative programming ; global optimization ; concave minimization ; efficient points ; heuristic algorithms ; multiple objectives
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Multiplicative programming problems are difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, finance, economics, and other fields. This article has two purposes. The first is to present an analysis that shows several relationships between concave multiplicative programs and concave minimization problems, and between concave multiplicative programs and certain multiple-objective mathematical programs. The second purpose is to propose and report computational results for a heuristic efficient-point search algorithm that we have designed for use on linear multiplicative programming problems. To our knowledge, this is the first heuristic algorithm of its type. The theoretical and algorithmic results given in the article offer some potentially important new avenues for analyzing and solving multiplicative programming problems of various types.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022600232285
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  • 2
    Electronic Resource
    Electronic Resource
    The Hyperbell Algorithm for Global Optimization: A Random Walk Using Cauchy Densities (1997)
    Springer
    Journal of global optimization 10 (1997), S. 37-55 
    Details
    ISSN: 1573-2916
    Keywords: global optimization ; random search ; Cauchy distributions.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article presents a new algorithm, called the’’Hyperbell Algorithm‘‘, that searches for the global extrema ofnumerical functions of numerical variables. The algorithm relies on theprinciple of a monotone improving random walk whose steps aregenerated around the current position according to a gradually scaleddown Cauchy distribution. The convergence of the algorithm is provenand its rate of convergence is discussed. Its performance is tested onsome ’’hard‘‘ test functions and compared to that of other recentalgorithms and possible variants. An experimental study of complexityis also provided, and simple tuning procedures for applications areproposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008230212303
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  • 3
    Electronic Resource
    Electronic Resource
    A Convex Envelope Formula for Multilinear Functions (1997)
    Springer
    Journal of global optimization 10 (1997), S. 425-437 
    Details
    ISSN: 1573-2916
    Keywords: Nonlinear 0–1 optimization ; linearization ; convex envelope ; concave extension ; bilinear programming ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Convex envelopes of multilinear functions on a unit hypercube arepolyhedral. This well-known fact makes the convex envelopeapproximation very useful in the linearization of non-linear 0–1programming problems and in global bilinear optimization. This paperpresents necessary and sufficient conditions for a convex envelope to be apolyhedral function and illustrates how these conditions may be used inconstructing of convex envelopes. The main result of the paper is a simpleanalytical formula, which defines some faces of the convex envelope of amultilinear function. This formula proves to be a generalization of the wellknown convex envelope formula for multilinear monomial functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008217604285
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  • 4
    Electronic Resource
    Electronic Resource
    Global Optima of Lennard-Jones Clusters (1997)
    Springer
    Journal of global optimization 11 (1997), S. 35-53 
    Details
    ISSN: 1573-2916
    Keywords: Molecular conformation ; global optimization ; Lennard-Jones cluster
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper summarizes the current state of knowledge concerning putative global minima of the potential energy function for Lennard-Jones clusters, an intensely studied molecular conformation problem. Almost all known exceptions to global optimality of the well-known Northby multilayer icosahedral conformations for microclusters are shown to be minor variants of that geometry. The truly exceptional case of face-centered cubic lattice conformations is examined and connections are made with the macrocluster problem. Several types of algorithms and their limitations are explored, and a new variation on the growth sequence idea is presented and shown to be effective for both small and large clusters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008276425464
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  • 5
    Electronic Resource
    Electronic Resource
    Weber‘s Problem with Attraction and Repulsion under Polyhedral Gauges (1997)
    Springer
    Journal of global optimization 11 (1997), S. 409-432 
    Details
    ISSN: 1573-2916
    Keywords: Location Theory ; global optimization ; discretization ; geometrical algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite set of points in the plane anda forbidden region $$\mathcal{R}$$ , we want to find a point $$X \notin \operatorname{int} (\mathcal{R})$$ , such thatthe weighted sum to all given points is minimized.This location problem is a variant of the well-known Weber Problem, where wemeasure the distance by polyhedral gauges and alloweach of the weights to be positive ornegative. The unit ballof a polyhedral gauge may be any convex polyhedron containingthe origin. This large class of distance functions allows verygeneral (practical) settings – such as asymmetry – to be modeled. Each given point isallowed to have its own gaugeand the forbidden region $$\mathcal{R}$$ enables us to include negative information in the model. Additionallythe use of negative and positive weights allows to include thelevel of attraction or dislikeness of a new facility.Polynomial algorithms and structural properties for this globaloptimization problem (d.c. objective function and anon-convex feasible set) based on combinatorial and geometrical methodsare presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008235107372
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  • 6
    Electronic Resource
    Electronic Resource
    Global Optimization of a Quadratic Functional with Quadratic Equality Constraints, Part 2 (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 547-556 
    Details
    ISSN: 1573-2878
    Keywords: Quadratic functionals ; quadratic equality constraints ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. It is assumed that the cost functional is positive definite and that the constraints are both feasible and regular (but otherwise they are unrestricted quadratic functions). Thus, the existence of a global constrained minimum is assured. We develop a necessary and sufficient condition that completely characterizes the global minimum cost. Such a condition is of essential importance in iterative numerical methods for solving the constrained minimization problem, because it readily distinguishes between local minima and global minima and thus provides a stopping criterion for the computation. The result is similar to one obtained previously by the authors. In the previous result, we gave a characterization of the global minimum of a constrained quadratic minimization problem in which the cost functional was an arbitrary quadratic functional (as opposed to positive-definite here) and the constraints were at least positive-semidefinite quadratic functions (as opposed to essentially unrestricted here).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022691012894
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  • 7
    Electronic Resource
    Electronic Resource
    Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 605-631 
    Details
    ISSN: 1573-2878
    Keywords: Multiple-objective optimization ; utility function programs ; global optimization ; branch-and-bound algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which amounts to a minimization over the efficient set when the utility function is increasing. A new algorithm is discussed for this utility function program which, under natural mild conditions, converges to an ∈-approximate global solution in a finite number of iterations. Applications include linear, convex, indefinite quadratic, Lipschitz, and d.c. objectives and constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022659523991
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  • 8
    Electronic Resource
    Electronic Resource
    Parallel Characteristical Algorithms for Solving Problems of Global Optimization (1997)
    Springer
    Journal of global optimization 10 (1997), S. 185-206 
    Details
    ISSN: 1573-2916
    Keywords: global optimization ; parallel computations ; characteristicalalgorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of parallel characteristical algorithms for global optimization ofone-dimensional multiextremal functions is introduced. General convergence andefficiency conditions for the algorithms of the class introduced areestablished. A generalization for the multidimensional case is considered.Examples of parallel characteristical algorithms and numerical experiments arepresented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008242328176
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  • 9
    Electronic Resource
    Electronic Resource
    Generalized Convex Multiplicative Programming via Quasiconcave Minimization (1997)
    Springer
    Journal of global optimization 10 (1997), S. 229-256 
    Details
    ISSN: 1573-2916
    Keywords: Generalized convex multiplicative programming ; conical partition ; global optimization ; branch-and-bound.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a new method for minimizing the sum of a convex function and aproduct of k nonnegative convex functions over a convex set. This problem isreduced to a k-dimensional quasiconcave minimization problem which is solvedby a conical branch-and-bound algorithm. Comparative computational results areprovided on test problems from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008203116882
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  • 10
    Electronic Resource
    Electronic Resource
    A Stochastic/Perturbation Global Optimization Algorithm for Distance Geometry Problems (1997)
    Springer
    Journal of global optimization 11 (1997), S. 91-105 
    Details
    ISSN: 1573-2916
    Keywords: Molecular conformation ; global optimization ; Lennard-Jones cluster
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a new global optimization approach for solving exactly or inexactly constrained distance geometry problems. Distance geometry problems are concerned with determining spatial structures from measurements of internal distances. They arise in the structural interpretation of nuclear magnetic resonance data and in the prediction of protein structure. These problems can be naturally formulated as global optimization problems which generally are large and difficult. The global optimization method that we present is related to our previous stochastic/perturbation global optimization methods for finding minimum energy configurations, but has several key differences that are important to its success. Our computational results show that the method readily solves a set of artificial problems introduced by Moré and Wu that have up to 343 atoms. On a set of considerably more difficult protein fragment problems introduced by Hendrickson, the method solves all the problems with up to 377 atoms exactly, and finds nearly exact solution for all the remaining problems which have up to 777 atoms. These preliminary results indicate that this approach has very good promise for helping to solve distance geometry problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008244930007
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  • 11
    Electronic Resource
    Electronic Resource
    A Hybrid Genetic Algorithm for Nonconvex Function Minimization (1997)
    Springer
    Journal of global optimization 11 (1997), S. 313-324 
    Details
    ISSN: 1573-2916
    Keywords: Nonconcex function ; global optimization ; genetic algorithms ; searchdirection ; Rosenbrock functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of minimizing a function in severalvariables which could be multimodal and may possess discontinuities. A newalgorithm for the problem based on the genetic technique is developed. Thealgorithm is hybrid in nature in the sense that it utilizes the genetictechnique to generate search directions, which are used in an optimizationscheme and is thus different from any other methods in the literature.The algorithm has been tested on the Rosenbrock valley functions in 2 and 4dimensions, and multimodal functions in 2 and 4 dimensions, which are of ahigh degree of difficulty. The results are compared with the Adaptive RandomSearch, and Simulated Annealing algorithms. The performance of the algorithmis also compared to recent global algorithms in terms of the number offunctional evaluations needed to obtain a global minimum and results show thatthe proposed algorithm is better than these algorithms on a set of standardtest problems. It seems that the proposed algorithm is efficient and robust.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008290611151
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  • 12
    Electronic Resource
    Electronic Resource
    Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces (1997)
    Springer
    Journal of global optimization 11 (1997), S. 341-359 
    Details
    ISSN: 1573-2916
    Keywords: Stochastic optimization ; nonlinear optimization ; global optimization ; genetic algorithm ; evolution strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008202821328
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  • 13
    Electronic Resource
    Electronic Resource
    A New Version of the Price's Algorithm for Global Optimization (1997)
    Springer
    Journal of global optimization 10 (1997), S. 165-184 
    Details
    ISSN: 1573-2916
    Keywords: global optimization ; eclipsing binary stars
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present an algorithm for finding a global minimum of a multimodal,multivariate function whose evaluation is very expensive, affected by noise andwhose derivatives are not available. The proposed algorithm is a new version ofthe well known Price's algorithm and its distinguishing feature is that ittries to employ as much as possible the information about the objectivefunction obtained at previous iterates. The algorithm has been tested on alarge set of standard test problems and it has shown a satisfactorycomputational behaviour. The proposed algorithm has been used to solveefficiently some difficult optimization problems deriving from the study ofeclipsing binary star light curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008250020656
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