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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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  • Tadeusz Antczak

    (University of Łódź)

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.

Suggested Citation

  • Tadeusz Antczak, 2021. "A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems," Computational Management Science, Springer, vol. 18(1), pages 49-71, January.
    • Handle: RePEc:spr:comgts:v:18:y:2021:i:1:d:10.1007_s10287-020-00379-0
    DOI: 10.1007/s10287-020-00379-0
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    References listed on IDEAS

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    1. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    2. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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