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

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Abstract

The aim of this paper is to provide necessary and sufficient conditions for a point to be an \(\epsilon \)-quasi solution of a scalar optimization problem via \(\epsilon \)-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 \(\epsilon \)-quasi efficient solutions of a vector equilibrium problem with constraints.

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  1. Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului 28, 400114, Cluj-Napoca, Romania

    Adela Capătă

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Capătă, A. Optimality conditions for \({\varvec{\epsilon }}\)-quasi solutions of optimization problems via \({\varvec{\epsilon }}\)-upper convexificators with applications. Optim Lett 13, 857–873 (2019). https://doi.org/10.1007/s11590-018-1287-1

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