Ekeland variational principles involving set perturbations in vector equilibrium problems

Le Phuoc Hai ()
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Le Phuoc Hai: University of Science

Journal of Global Optimization, 2021, vol. 79, issue 3, No 9, 733-756

Abstract: 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.

Keywords: Ekeland variational principle; Set perturbations; Approximate proper efficiency; Approximating family of cones; Multiobjective programming; Variational inequalities; 90C33; 90C26; 90C29; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00945-5

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