WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Solving the Class of Nonsmooth Nonconvex Fuzzy Optimization Problems via the Absolute Value Exact Fuzzy Penalty Function Method
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Abstract: In recent years, in optimization theory, there has been a growing use of optimization models of real decision-making processes related to the activities of modern humans, in which the hypotheses are not verifiable in a way typical of classical optimization. This increases the demand for tools that will enable the effective solving of such more real optimization models. Fuzzy optimization problems were developed to model real-world extremum problems with uncertainty, which means that they are not usually well-defined. In this work, we investigate one of such tools, i.e. the absolute value exact fuzzy penalty function method which is applied to solve invex nonsmooth minimization problems with fuzzy objective functions and inequality (crisp) constraints. Namely, we analyze the exactness of the penalization which is the most important property of any such method from a practical point of view. Further, the algorithm of the absolute value exact penalty function method is presented in the context of finding weakly nondominated solutions of the analyzed nonsmooth fuzzy optimization problem and, moreover, its convergence is proven in the considered fuzzy case. Finally, we also simulate the choice of the penalty parameter in the aforesaid algorithm.
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Keywords: fuzzy optimization, nondifferentiable optimization problem with the fuzzy objective function, Clarke generalized gradient, Karush-Kuhn-Tucker optimality conditions, nondominated solution, absolute value exact penalty function method, exactness of the penalization, invex fuzzy function
Pages: 408-429
DOI: 10.37394/23206.2024.23.44