1. Ekeland variational principles involving set perturbations in vector equilibrium problems
- Author
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Le Phuoc Hai
- Subjects
021103 operations research ,Control and Optimization ,Basis (linear algebra) ,Applied Mathematics ,Linear space ,0211 other engineering and technologies ,Hausdorff space ,02 engineering and technology ,Management Science and Operations Research ,Space (mathematics) ,Computer Science Applications ,Variational principle ,Variational inequality ,Applied mathematics ,Mathematics ,Vector space ,Normed vector space - 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.
- Published
- 2020
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