Full Text: PDF
DOI: 10.23952/cot.2023.32
Received November 12, 2022; Accepted March 31, 2023; Published July 3, 2023
Abstract. Vector equilibrium problems are a natural generalization to the context of partially ordered spaces of the Ky Fan inequality, where scalar bifunctions are replaced with vector bifunctions. In the present paper, the local geometry of the strong solution set to these problems is investigated through its inner/outer conical approximations. More precisely, formulae for approximating the contingent cone to the set of strong vector equilibria are established, which are expressed via Bouligand derivatives of the bifunctions. These results are subsequently employed for deriving both necessary and sufficient optimality conditions for problems, whose feasible region is the strong solution set to a vector equilibrium problem, so they can be cast in mathematical programming with equilibrium constraints.
How to Cite this Article:
A. Uderzo, First-order approximation of strong vector equilibria with application to nondifferentiable constrained optimization, Commun. Optim. Theory 2023 (2023) 32.