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

Tadeusz Antczak ()
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Tadeusz Antczak: University of Łódź

Computational Management Science, 2021, vol. 18, issue 1, No 3, 49-71

Abstract: 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 $$(\Phi ,\rho )$$ ( Φ , ρ ) -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.

Keywords: Multiobjective programming; Approximated vector optimization problem; (weak) Pareto solution; Optimality conditions; $$(\Phi; \rho )$$ ( Φ; ρ ) -invexity; Mond-Weir duality; 90C29; 90C46; 90C59; 90C26 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10287-020-00379-0

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