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The Exactness Property of the vector Exact l₁ Penalty Function Method in Nondifferentiable Invex Multiobjective Programming

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NUMERICAL FUNCTIONAL ANALYSIS AND optimization 2016年第12期37卷 1465-1487页

作者： Antczak, Tadeusz Studniarski, Marcin Univ Lodz Dept Math & Comp Sci Lodz Poland

In this article, the vector exact l(1) penalty function method used for solving nonconvex nondifferentiable multiobjective program ming problems is analyzed. In this method, the vector penalized optimization problem with the vector exact l(1) penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l(1) penalty function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article.

关键词： Invex function multiobjective programming penalized vector optimization problem vector exact l(1) penalty function (weak) Pareto optimal point

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The vector exact l₁ penalty method for nondifferentiable convex multiobjective programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2012年第18期218卷 9095-9106页

作者： Antczak, Tadeusz Univ Lodz Fac Math & Comp Sci PL-90238 Lodz Poland

In this paper, the vector exact l(1) penalty function method for nondifferentiable convex multiobjective programming problems is analyzed. The vector penalized optimization problem with the vector exact l(1) penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l(1) penalty function. This equivalence is established for nondifferentiable vector optimization problems with convex functions. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Multiobjective programming (Weak) Pareto optimal point vector exact l(1) penalty function penalized vector optimization problem Convex function

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vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming problems

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2018年第2期41卷 657-686页

作者： Antczak, Tadeusz Univ Lodz Fac Math & Comp Sci Banacha 22 PL-90238 Lodz Poland

In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of this method is established. Further, the exactness property of a vector exact penalty function method is defined and analyzed in the context of the introduced vector exponential penalty function method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential penalty function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving functions are r-invex.

关键词： Multiobjective programming (weak) Pareto solution vector exact exponential penalty function penalized vector optimization problem r-Invex function

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