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Journal of Global Optimization

, Volume 3, Issue 3, pp 311–324 | Cite as

A generalized duality and applications

  • Phan Thien Thach
Article

Abstract

The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.

Key words

Nonconvex duality zero gap global optimization 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Phan Thien Thach
    • 1
  1. 1.Institute of Human and Social SciencesTokyo Institute of TechnologyJapan

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