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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1002/ajmg.a.20626

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1573-2878

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Optimality Conditions for Disjunctive Optimization

Authors: Wen Song Qianqian Wang
Publish Date: 2014/05/06
Volume: 164, Issue: 2, Pages: 436-454
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Abstract

We study optimization problems with the constraints having disjunctive structures in reflexive Banach spaces By the representations of contingent cones and Fréchet normal cones to finite unions of sets in general Banach spaces and using the special structures of convex generalized polyhedral sets we calculate the Mordukhovich normal cones to finite unions of closed and convex sets that particularly include convex generalized polyhedral sets in reflexive Banach spaces Furthermore based on these calculations and the Guignardtype constraint qualifications we derive new optimality conditions for disjunctive optimization problems We also present specializations of these results to optimization problems with variational inequality constraintsThe authors are grateful to the anonymous referees who have contributed to improve the quality of the paper The research was partially supported by the National Natural Sciences Grant No 11071052 and the Scientific Innovation Project for Graduate of Heilongjiang Province No YJSCX2012160HLJ

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