Some constraint qualifications for quasiconvex vector-valued systems

Satoshi Suzuki () and Daishi Kuroiwa ()

Journal of Global Optimization, 2013, vol. 55, issue 3, 539-548

Abstract: In this paper, we consider minimization problems with a quasiconvex vector-valued inequality constraint. We propose two constraint qualifications, the closed cone constraint qualification for vector-valued quasiconvex programming (the VQ-CCCQ) and the basic constraint qualification for vector-valued quasiconvex programming (the VQ-BCQ). Based on previous results by Benoist et al. (Proc Am Math Soc 13:1109–1113, 2002 ), and Suzuki and Kuroiwa (J Optim Theory Appl 149:554–563, 2011 ), and (Nonlinear Anal 74:1279–1285, 2011 ), we show that the VQ-CCCQ (resp. the VQ-BCQ) is the weakest constraint qualification for Lagrangian-type strong (resp. min–max) duality. As consequences of the main results, we study semi-definite quasiconvex programming problems in our scheme, and we observe the weakest constraint qualifications for Lagrangian-type strong and min–max dualities. Finally, we summarize the characterizations of the weakest constraint qualifications for convex and quasiconvex programming. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Quasiconvex programming; Quasiaffine functions; Vector-valued; Constraint qualification; 90C26; 26B25 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10898-011-9807-x

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