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  • Artikel  (14)
  • global optimization  (14)
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  • Springer  (14)
  • American Meteorological Society
  • American Physical Society (APS)
  • Blackwell Publishing Ltd
  • De Gruyter
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  • 1995-1999  (13)
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  • 1
    Digitale Medien
    Digitale Medien
    Bayesian testing of nonparametric hypotheses and its application to global optimization (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 31-50 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Bayesian testing ; nonparametric inference ; random distribution functions ; global optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Random distribution functions are the basic tool for solving nonparametric decision-theoretic problems. In 1974, Doksum introduced the family of distributions neutral to the right, that is, distributions such thatF(t 1),[F(t 2)−F(t 1)]/[1 −F(t 1)],...,[F(t k)−F(t k − 1)]/[1 −F(t k − 1)] are independent whenevert 1 〈 ... 〈t kIn practice, application of distributions neutral to the right has been prevented by the lack of a manageable analytical expression for probabilities of the typeP(F(t)〈q) for fixedt andq. A subclass of such distributions can be provided which allows for a close expression of the characteristic function of log[1−F(t)], given the sample. Then, thea posteriori distribution ofF(t) is obtained by numerical evaluation of a Fourier integral. As an application, the global optimization problem is formulated as a problem of inference about the quantiles of the distributionF(y) of the random variableY=f(X), wheref is the objective function andX is a random point in the search domain.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934132
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Multiplicative programming ; global optimization ; concave minimization ; efficient points ; heuristic algorithms ; multiple objectives
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022600232285
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): global optimization ; random search ; Cauchy distributions.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008230212303
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  • 4
    Digitale Medien
    Digitale Medien
    A Convex Envelope Formula for Multilinear Functions (1997)
    Springer
    Journal of global optimization 10 (1997), S. 425-437 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Nonlinear 0–1 optimization ; linearization ; convex envelope ; concave extension ; bilinear programming ; global optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008217604285
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  • 5
    Digitale Medien
    Digitale Medien
    Global Optima of Lennard-Jones Clusters (1997)
    Springer
    Journal of global optimization 11 (1997), S. 35-53 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Molecular conformation ; global optimization ; Lennard-Jones cluster
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008276425464
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  • 6
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Location Theory ; global optimization ; discretization ; geometrical algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008235107372
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  • 7
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Quadratic functionals ; quadratic equality constraints ; global optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022691012894
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  • 8
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Multiple-objective optimization ; utility function programs ; global optimization ; branch-and-bound algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022659523991
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  • 9
    Digitale Medien
    Digitale Medien
    Parallel Characteristical Algorithms for Solving Problems of Global Optimization (1997)
    Springer
    Journal of global optimization 10 (1997), S. 185-206 
    Details
    ISSN: 1573-2916
    Schlagwort(e): global optimization ; parallel computations ; characteristicalalgorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008242328176
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  • 10
    Digitale Medien
    Digitale Medien
    Generalized Convex Multiplicative Programming via Quasiconcave Minimization (1997)
    Springer
    Journal of global optimization 10 (1997), S. 229-256 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Generalized convex multiplicative programming ; conical partition ; global optimization ; branch-and-bound.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008203116882
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