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Enumerative techniques for solving some nonconvex global optimization problems

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Summary

We give an overview on different methods for solving nonconvex minimization problems using techniques of enumeration of extreme points. The problems considered include concave, indefinite quadratic, and special structured problems such as the concave cost network flow problem and linear complementarity. For methods that enumerate the extreme points according to the ascending order of the value of a linear underestimating function we propose new techniques for obtaining such underestimators.

Zusammenfassung

Wir geben einen Überblick über verschiedene Methoden für nicht konvexe Minimisierungsaufgaben. Insbesondere diskutieren wir Aufzählungsmethoden für Extrempunkte. Wir betrachten konkave, quadratisch indefinite Probleme ebenso wie Probleme spezieller Struktur: konkave Netzwerk-Fluß-Probleme und lineare Komplementaritäts-Probleme. Wir schlagen neue Methoden vor, um lineare untere Schranken für Aufzählungstechnicken zu erhalten.

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Authors and Affiliations

  1. Computer Science Department, The Pennsylvania State University, 16802, University Park, PA, USA

    P. M. Pardalos

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  1. P. M. Pardalos
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Pardalos, P.M. Enumerative techniques for solving some nonconvex global optimization problems. OR Spektrum 10, 29–35 (1988). https://doi.org/10.1007/BF01720032

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  • DOI: https://doi.org/10.1007/BF01720032

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