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Quasiconvex Minimization on a Locally Finite Union of Convex Sets

Author

Listed:
  • D. Aussel

    (Université de Perpignan)

  • J. J. Ye

    (University of Victoria)

Abstract

Extending the approach initiated in Aussel and Hadjisavvas (SIAM J. Optim. 16:358–367, 2005) and Aussel and Ye (Optimization 55:433–457, 2006), we obtain the existence of a local minimizer of a quasiconvex function on the locally finite union of closed convex subsets of a Banach space. We apply the existence result to some difficult nonconvex optimization problems such as the disjunctive programming problem and the bilevel programming problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9431-1
    DOI: 10.1007/s10957-008-9431-1
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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. Egon Balas, 2005. "Projection, Lifting and Extended Formulation in Integer and Combinatorial Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 125-161, November.
    3. H. T. Jongen & J. J. Rückmann & O. Stein, 1997. "Disjunctive Optimization: Critical Point Theory," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 321-336, May.
    4. Jane J. Ye, 2006. "Constraint Qualifications and KKT Conditions for Bilevel Programming Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 811-824, November.
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    Cited by:

    1. 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.
    2. D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    3. D. Aussel & J. Cotrina, 2011. "Semicontinuity of the solution map of quasivariational inequalities," Journal of Global Optimization, Springer, vol. 50(1), pages 93-105, May.

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