On Standard Quadratic Optimization Problems

Authors:
Immanuel M. Bomze
Affiliations:
I.S.O.C., University of Vienna, Wien, Austria
Venue:
Journal of Global Optimization
Year:
1998

Citing 15
Cited 22

On the maximum weight clique problem

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Stereo Correspondence Through Feature Grouping and Maximal Cliques

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Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs

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A sublinear-time randomized parallel algorithm for the maximum clique problem in perfect graphs

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Detecting all evolutionarily stable strategies

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Hierarchical stereo and motion correspondence using feature groupings

International Journal of Computer Vision
Relaxation labeling networks for the maximum clique problem

Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Feasible and infeasible maxima in a quadratic program for maximum clique

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Continuous characterizations of the maximum clique problem

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Two Algorithms for Determining Volumes of Convex Polyhedra

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Computer Vision

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Global and LocalQuadratic Minimization

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Evolution towards the Maximum Clique

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Global Escape Strategies for Maximizing QuadraticForms over a Simplex

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Introduction to Global Optimization (Nonconvex Optimization and Its Applications)

Introduction to Global Optimization (Nonconvex Optimization and Its Applications)

Matching Hierarchical Structures Using Association Graphs

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A New Semidefinite Programming Bound for Indefinite Quadratic Forms Over a Simplex

Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems

Journal of Global Optimization
Convex Quadratic Programming Approachto the Maximum Matching Problem

Journal of Global Optimization
Convex Quadratic Programming Approach to the Maximum Matching Problem

Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems

Journal of Global Optimization
A class of problems where dual bounds beat underestimation bounds

Journal of Global Optimization
Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming

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A Complementary Pivoting Approach to Graph Matching

EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Undominated d.c. Decompositions of Quadratic Functions and Applications to Branch-and-Bound Approaches

Computational Optimization and Applications
Improving an Upper Bound on the Stability Number of a Graph

Journal of Global Optimization
Quartic Formulation of Standard Quadratic Optimization Problems

Journal of Global Optimization
Payoff-Monotonic Game Dynamics and the Maximum Clique Problem

Neural Computation
A clique algorithm for standard quadratic programming

Discrete Applied Mathematics
Complementary approaches for the computation of the independent number of a graph

MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation

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Computing Nash equilibria gets harder: new results show hardness even for parameterized complexity

CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Properties of two DC algorithms in quadratic programming

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An improved algorithm to test copositivity

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Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization

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Standard bi-quadratic optimization problems and unconstrained polynomial reformulations

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Tightening a copositive relaxation for standard quadratic optimization problems

Computational Optimization and Applications

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Abstract

A standard quadratic optimization problem (QP) consists of finding(global) maximizers of a quadratic form over the standard simplex. StandardQPs arise quite naturally in copositivity-based procedures which enable anescape from local solutions. Furthermore, several important applicationsyield optimization problems which can be cast into a standard QP in astraightforward way. As an example, a new continuous reformulation of themaximum weight clique problem in undirected graphs is presented whichconsiderably improves previous attacks both as numerical stability andinterpretation of the results are concerned. Apparently also for the firsttime, an equivalence between standard QPs and QPs on the positive orthant isestablished. Also, a recently presented global optimization procedure (GENF- genetical engineering via negative fitness) is shortly reviewed.