Journal: Journal of Global Optimization

Abbreviation

J. glob. optim.

Publisher

Springer

Journal Volumes

ISSN

0925-5001
1573-2916

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Publications 1 - 7 of 7
  • An adaptive algorithm for vector partitioning
    Item type: Journal Article
    Fukuda, Komei; Onn, Shmuel; Rosta, Vera (2003)
    Journal of Global Optimization
  • Convergence of stochastic search algorithms to finite size pareto set approximations
    Item type: Journal Article
    Schütze, Oliver; Laumanns, Marco; Coello, Carlos A.; et al. (2008)
    Journal of Global Optimization
  • A branch and bound method for the solution of multiparametric mixed integer linear programming problems
    Item type: Journal Article
    Oberdieck, Richard; Wittmann-Hohlbein, Martina; Pistikopoulos, Efstratios N. (2014)
    Journal of Global Optimization
  • Three enhancements for optimization-based bound tightening
    Item type: Journal Article
    Gleixner, Ambros M.; Berthold, Timo; Müller, Benjamin; et al. (2017)
    Journal of Global Optimization
  • On generalized KKT points for the Motzkin–Straus program
    Item type: Journal Article
    Beretta, Guglielmo; Torcinovich, Alessandro; Pelillo, Marcello (2025)
    Journal of Global Optimization
    In 1965, T.S. Motzkin and E. G. Straus established an elegant connection between the clique number of a graph and the global maxima of a quadratic program defined on the standard simplex. Over the years, this seminal finding has inspired a number of studies aimed at characterizing the properties of the (local and global) solutions of the Motzkin–Straus program. The result has also been generalized in various ways and has served as the basis for establishing new bounds on the clique number and developing powerful clique-finding heuristics. Despite the extensive work done on the subject, apart from a few exceptions, the existing literature pays little or no attention to the Karush–Kuhn–Tucker (KKT) points of the program. In the conviction that these points might reveal interesting structural properties of the graph underlying the program, this paper tries to fill in the gap. In particular, we study the generalized KKT points of a parameterized version of the Motzkin–Straus program, which are defined via a relaxation of the usual first-order optimality conditions, and we present a number of results that shed light on the symmetries and regularities of certain substructures associated with the underlying graph. These combinatorial structures are further analyzed using barycentric coordinates, thereby providing a link to a related quadratic program that encodes local structural properties of the graph. This turns out to be particularly useful in the study of the generalized KKT points associated with a certain class of graphs that generalize the notion of a star graph. Finally, we discuss the associations between the generalized KKT points of the Motzkin–Straus program and the so-called replicator dynamics, thereby offering an alternative, dynamical-system perspective on the results presented in the paper.
  • Some properties of a hypergeometric function which appear in an approximation problem
    Item type: Journal Article
    Milanovic, Gradimir V.; Rassias, Michael Th. (2013)
    Journal of Global Optimization
  • Extended formulations for convex envelopes
    Item type: Journal Article
    Ballerstein, Martin; Michaels, Dennis (2014)
    Journal of Global Optimization
    In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30 % of all nonlinearities in common benchmark libraries. To overcome the combinatorial difficulties in deriving the convex envelope description given by the component-wise concave part of the functions, we consider an extended formulation of the convex envelope based on the Reformulation–Linearization-Technique introduced by Sherali and Adams (SIAM J Discret Math 3(3):411–430, 1990). Computational results are reported showing that the extended formulation strategy is a useful tool in global optimization.
Publications 1 - 7 of 7