Optimality conditions for invex nonsmooth optimization problems with fuzzy objective functions

In this paper, the definitions of Clarke generalized directional 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 cons...

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Published in:Fuzzy optimization and decision making Vol. 22; no. 1; pp. 1 - 21
Main Author: Antczak, Tadeusz
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2023
Springer Nature B.V
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Fuzzy sets
Inequality
Kuhn-Tucker method
Mathematical Logic and Foundations
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Probability Theory and Stochastic Processes
Weighting methods
Nonsmooth optimization problem with fuzzy objective function
Weighting method
Nondominated solution
Invex fuzzy function
Karush-Kuhn-Tucker optimality conditions
ISSN:1568-4539, 1573-2908
Online Access:Get full text
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Summary:In this paper, the definitions of Clarke generalized directional 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.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-022-09381-4