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Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces

Author

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  • Wen Song

    (School of Mathematical Sciences, Harbin Normal University)

  • Qianqian Wang

    (School of Mathematical Sciences, Harbin Normal University)

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 Guignard-type constraint qualifications, we derive new optimality conditions for disjunctive optimization problems. We also present specializations of these results to optimization problems with variational inequality constraints.

Suggested Citation

  • Wen Song & Qianqian Wang, 2015. "Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 436-454, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0571-1
    DOI: 10.1007/s10957-014-0571-1
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    References listed on IDEAS

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    1. M. Gugat, 1997. "Parametric Disjunctive Programming: One-Sided Differentiability of the Value Function," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 285-310, February.
    2. D. Aussel & J. J. Ye, 2008. "Quasiconvex Minimization on a Locally Finite Union of Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 1-16, October.
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