Optimality conditions for invex nonsmooth optimization problems with fuzzy objective functions

Tadeusz Antczak ()
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Tadeusz Antczak: University of Łódź

Fuzzy Optimization and Decision Making, 2023, vol. 22, issue 1, No 1, 21 pages

Abstract: Abstract In this paper, the definitions of Clarke generalized directional $$\alpha $$ α -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem.

Keywords: Nonsmooth optimization problem with fuzzy objective function; Karush-Kuhn-Tucker optimality conditions; Nondominated solution; Weighting method; Invex fuzzy function (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10700-022-09381-4

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