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eng
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Description | In this paper, we consider minimization problems with a quasiconvex vector-valued inequality constraint. We propose two constraint quali12;cations, the closed cone constraint quali12;cation for vector-valued quasiconvex programming (the VQ-CCCQ) and the basic constraint quali12;cation for vector-valued quasicon-vex programming (the VQ-BCQ). Based on previous results by Benoist, Borwein, and Popovici (Proc. Amer. Math. Soc. 13: 1109-1113, 2002), and the authors (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 quali12;cation 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.
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Subject | quasiconvex programming
quasiaffine functions
vector-valued
constraint qualification
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Journal Title |
Journal of Global Optimization
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Volume | 55
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Issue | 3
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Start Page | 539
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End Page | 548
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ISSN | 09255001
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Published Date | 2013-03
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DOI | |
DOI Date | 2015-07-14
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NCID | AA10831465
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Publisher | Springer US
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NII Type |
Journal Article
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Format |
PDF
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Rights | © Springer Science+Business Media, LLC. 2011
The final publication is available at Springer via http://dx.doi.org/10.1007/s10898-011-9807-x.
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Text Version |
著者版
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OAI-PMH Set |
Interdisciplinary Graduate School of Science and Engineering
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