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A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems

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Abstract

In this paper, a new approximation method for a characterization of (weak) Pareto solutions in some class of nonconvex differentiable multiobjective programming problems is introduced. In this method, an auxiliary approximated vector optimization problem is constructed at a given feasible solution of the original multiobjective programming problem. The equivalence between (weak) Pareto solutions of these two vector optimization problems is established under \((\Phi ,\rho )\)-invexity hypotheses. By using the introduced approximation method, it is shown in some cases that a nonlinear differentiable multiobjective programming problem can be solved by the help of some methods for solving a linear vector optimization problem. Further, the introduced approximation method is used in proving several duality results in the sense of Mond-Weir for the considered vector optimization problem.

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  1. Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238, Łódź, Poland

    Tadeusz Antczak

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  1. Tadeusz Antczak
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Antczak, T. A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems. Comput Manag Sci 18, 49–71 (2021). https://doi.org/10.1007/s10287-020-00379-0

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