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Projective dualities for quasiconvex problems

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  • Jean-Paul Penot

Abstract

We study two dualities that can be applied to quasiconvex problems. They are conjugacies deduced from polarities. They are characterized by the polar sets of sublevel sets. We give some calculus rules for the associated subdifferentials and we relate the subdifferentials to known subdifferentials. We adapt the general duality schemes in terms of Lagrangians or in terms of perturbations to two specific problems. First a general mathematical programming problem and then a programming problem with linear constraints. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Jean-Paul Penot, 2015. "Projective dualities for quasiconvex problems," Journal of Global Optimization, Springer, vol. 62(3), pages 411-430, July.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:411-430
    DOI: 10.1007/s10898-014-0261-4
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    References listed on IDEAS

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    1. J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
    2. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
    3. Jean-Paul Penot, 2005. "Unilateral Analysis and Duality," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 1-37, Springer.
    4. Harvey J. Greenberg & William P. Pierskalla, 1971. "A Review of Quasi-Convex Functions," Operations Research, INFORMS, vol. 19(7), pages 1553-1570, December.
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