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Optimality conditions for convex problems on intersections of non necessarily convex sets

Author

Listed:
  • E. Allevi

    (Università degli Studi di Brescia)

  • J. E. Martínez-Legaz

    (Universitat Autònoma de Barcelona
    BGSMath)

  • R. Riccardi

    (Università degli Studi di Brescia)

Abstract

We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500–510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.

Suggested Citation

  • E. Allevi & J. E. Martínez-Legaz & R. Riccardi, 2020. "Optimality conditions for convex problems on intersections of non necessarily convex sets," Journal of Global Optimization, Springer, vol. 77(1), pages 143-155, May.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:1:d:10.1007_s10898-019-00849-z
    DOI: 10.1007/s10898-019-00849-z
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    References listed on IDEAS

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    1. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.
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    Cited by:

    1. Nguyen Canh Hung & Thai Doan Chuong & Nguyen Le Hoang Anh, 2024. "Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 771-794, August.

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