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Title of Journal: J Glob Optim

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Abbravation: Journal of Global Optimization

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Springer US

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DOI

10.1007/bf02234192

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1573-2916

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Some constraint qualifications for quasiconvex vec

Authors: Satoshi Suzuki Daishi Kuroiwa
Publish Date: 2011/11/08
Volume: 55, Issue: 3, Pages: 539-548
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Abstract

In this paper we consider minimization problems with a quasiconvex vectorvalued inequality constraint We propose two constraint qualifications the closed cone constraint qualification for vectorvalued quasiconvex programming the VQCCCQ and the basic constraint qualification for vectorvalued quasiconvex programming the VQBCQ Based on previous results by Benoist et al Proc Am Math Soc 131109–1113 2002 and Suzuki and Kuroiwa J Optim Theory Appl 149554–563 2011 and Nonlinear Anal 741279–1285 2011 we show that the VQCCCQ resp the VQBCQ is the weakest constraint qualification for Lagrangiantype strong resp min–max duality As consequences of the main results we study semidefinite quasiconvex programming problems in our scheme and we observe the weakest constraint qualifications for Lagrangiantype strong and min–max dualities Finally we summarize the characterizations of the weakest constraint qualifications for convex and quasiconvex programming

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