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Ekeland variational principles involving set perturbations in vector equilibrium problems

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  • Le Phuoc Hai

    (University of Science
    Vietnam National University)

Abstract

On the basis of the notion of approximating family of cones and a generalized type of Gerstewitz’s/Tammer’s nonlinear scalarization functional, we establish variants of the Ekeland variational principle (for short, EVP) involving set perturbations for a type of approximate proper solutions in the sense of Henig of a vector equilibrium problem. Initially, these results are obtained for both an unconstrained and a constrained vector equilibrium problem, where the objective function takes values in a real locally convex Hausdorff topological linear space. After that, we consider special cases when the objective function takes values in a normed space and in a finite-dimensional vector space. For the finite-dimensional objective space with a polyhedral ordering cone, we give the explicit representation of variants of EVP depending on matrices, and in such a way, some selected applications for multiobjective optimization problems and vector variational inequality problems are also derived.

Suggested Citation

  • Le Phuoc Hai, 2021. "Ekeland variational principles involving set perturbations in vector equilibrium problems," Journal of Global Optimization, Springer, vol. 79(3), pages 733-756, March.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00945-5
    DOI: 10.1007/s10898-020-00945-5
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    References listed on IDEAS

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    1. X. H. Gong, 2007. "Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 151-161, May.
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