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Parametric Disjunctive Programming: One-Sided Differentiability of the Value Function

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  • M. Gugat

    (University of Trier)

Abstract

We consider a countable family of one-parameter convex programs and give sufficient conditions for the one-sided differentiability of its optimal value function. The analysis is based on the Borwein dual problem for a family of convex programs (a convex disjunctive program). We give conditions that assure stability of the situation of perfect duality in the Borwein theory. For the reader's convenience, we start with a review of duality results for families of convex programs. A parametric family of dual problems is introduced that contains the dual problems of Balas and Borwein as special cases. In addition, a vector optimization problem is defined as a dual problem. This generalizes a result by Helbig about families of linear programs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:2:d:10.1023_a:1022603112856
    DOI: 10.1023/A:1022603112856
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    References listed on IDEAS

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    1. Daniel Granot & Frieda Granot & Ellis L. Johnson, 1982. "Duality and Pricing in Multiple Right-Hand Choice Linear Programming Problems," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 545-556, November.
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    Cited by:

    1. 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.
    2. 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.

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