459 research outputs found
First-order approximation of strong vector equilibria with application to nondifferentiable constrained optimization
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. 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
Merit functions: a bridge between optimization and equilibria
In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented
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