Some constraint qualifications for quasiconvex vector-valued systems

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• 作者：Satoshi Suzuki (1)
  Daishi Kuroiwa (1)
  
• 关键词：Quasiconvex programming ; Quasiaffine functions ; Vector ; valued ; Constraint qualification ; 90C26 ; 26B25
• 刊名：Journal of Global Optimization
• 出版年：2013
• 出版时间：March 2013
• 年：2013
• 卷：55
• 期：3
• 页码：539-548
• 全文大小：169 KB
• 参考文献：1. Jeyakumar, V., Dinh, N., Lee, G.M.: A new closed cone constraint qualification for convex optimization. Research Report AMR 04/8, Department of Applied Mathematics, University of New South Wales (2004)
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  3. Li C., Ng K.F., Pong T.K.: Constraint qualifications for convex inequality systems with applications in constrained optimization. SIAM J. Optim. 19, 163-87 (2008) CrossRef
  4. Suzuki S., Kuroiwa D.: On set containment characterization and constraint qualification for quasiconvex programming. J. Optim. Theory Appl. 149, 554-63 (2011) CrossRef
  5. Suzuki S., Kuroiwa D.: Optimality conditions and the basic constraint qualification for quasiconvex programming. Nonlinear Anal. 74, 1279-285 (2011) CrossRef
  6. Penot J.P., Volle M.: On quasi-convex duality. Math. Oper. Res. 15, 597-25 (1990) CrossRef
  7. Benoist J., Borwein J.M., Popovici N.: A characterization of quasiconvex vector-valued functions. Proc. Am. Math. Soc. 13, 1109-113 (2002)
  8. Bo? R.I., Wanka G.: An alternative formulation for a new closed conlification. Nonlinear Anal. 64, 1367-381 (2006) CrossRef
  9. Goberna M.A., Jeyakumar V., López M.A.: Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities. Nonlinear Anal. 68, 1184-194 (2008) CrossRef
  
• 作者单位：Satoshi Suzuki (1)
  Daishi Kuroiwa (1)
  
  1. Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue, Shimane, Japan
  
• ISSN：1573-2916

文摘

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 13:1109-113, 2002), and Suzuki and Kuroiwa (J Optim Theory Appl 149:554-63, 2011), and (Nonlinear Anal 74:1279-285, 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.