Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints

Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints

In this paper, we present some new necessary and sufficient optimality conditions in terms of Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the par...

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Veröffentlicht in:Acta mathematica vietnamica 2020-06, Vol.45 (2), p.435-448
Hauptverfasser: Son, Ta Quang, Van Tuyen, Nguyen, Wen, Ching-Feng
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Constraints
Mathematical programming
Mathematics
Mathematics and Statistics
Nonlinear programming
Optimization
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description In this paper, we present some new necessary and sufficient optimality conditions in terms of Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the particular cases of cone-constrained convex vector optimization problems and semidefinite vector optimization problems. Examples are given to illustrate the obtained results.
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subjects Constraints
Mathematical programming
Mathematics
Mathematics and Statistics
Nonlinear programming
Optimization
title Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints
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