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Optimality conditions for $${\varvec{\epsilon }}$$ϵ-quasi solutions of optimization problems via $${\varvec{\epsilon }}$$ϵ-upper convexificators with applications

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The aim of this paper is to provide necessary and sufficient conditions for a point to be an $$\epsilon $$ϵ-quasi solution of a scalar optimization problem via $$\epsilon $$ϵ-convexificators. Then,… Click to show full abstract

The aim of this paper is to provide necessary and sufficient conditions for a point to be an $$\epsilon $$ϵ-quasi solution of a scalar optimization problem via $$\epsilon $$ϵ-convexificators. Then, the main results are applied in order to obtain necessary conditions for approximate solutions of a vector optimization problem with constraints, which, at its turn, provides necessary conditions for $$\epsilon $$ϵ-quasi efficient solutions of a vector equilibrium problem with constraints.

Keywords: optimization; varvec epsilon; epsilon; conditions varvec; optimality conditions; epsilon quasi

Journal Title: Optimization Letters
Year Published: 2019

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