The exponential penalty function method for multiobjective programming problems

Liu, Sanming; Feng, Enmin

doi:10.1080/10556780903049959

Cited by 16 publications

(20 citation statements)

References 6 publications

(6 reference statements)

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“…holds, contradicting (27). This means that any limit point of any convergence subsequence of (x n ) is a weak Pareto solution in the considered multiobjective programming problem (VP).…”

Section: Convergence Of a New Vector Exponential Penalty Function Metmentioning

confidence: 72%

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Vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming Problems

Antczak

2016

Bull. Malays. Math. Sci. Soc.

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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.Keywords Multiobjective programming · (weak) Pareto solution · Vector exact exponential penalty function · Penalized vector optimization problem · r -Invex function Mathematics Subject Classification 49M37 · 90C29 · 90C30 · 90C26 Communicated by

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“…holds, contradicting (27). This means that any limit point of any convergence subsequence of (x n ) is a weak Pareto solution in the considered multiobjective programming problem (VP).…”

Section: Convergence Of a New Vector Exponential Penalty Function Metmentioning

confidence: 72%

“…Exponential penalty function methods have been used widely in optimization theory by several authors for solving optimization problems of various types (see, for example, [21][22][23][24][25][26][27][28][29], and others).…”

Section: Introductionmentioning

confidence: 99%

Vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming Problems

Antczak

2016

Bull. Malays. Math. Sci. Soc.

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“…Murphy [11] developed a class of exponential penalty functions for nonlinear program and established its convergence rate. Recently, Liu and Feng [8] constructed exponential penalty function method for multiobjective programming problems and proved its convergence.…”

Section: Introductionmentioning

confidence: 99%

“…The class of penalty functions has been studied by many researchers, see for instance, [1,2,[8][9][10][11][12]. Murphy [11] developed a class of exponential penalty functions for nonlinear program and established its convergence rate.…”

Section: Introductionmentioning

confidence: 99%

Convergence of exponential penalty function method for multiobjective fractional programming problems

Jayswal

Choudhury

2014

Ain Shams Engineering Journal

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In this paper, we extend the application of exponential penalty function method for solving multiobjective programming problem introduced by Liu and Feng (2010) to solve multiobjective fractional programming problem and analyze the relationship between weak efficient solutions of penalized problems and multiobjective fractional programming problem. Furthermore, we examine the convergence of this method for multiobjective fractional programming problems.Ó 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

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“…In return, this sequence of problems yields a sequence of optimal solutions, which approaches the optimal solution of the constrained mathematical optimization problem. Liu and Feng [1] proved the convergence of exponential penalty function method for solving multiobjective optimization problems, and solved the finite min-max multiobjective optimization problem.…”

Section: Introductionmentioning

confidence: 99%

An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems

Jayswal

Choudhury

2015

J Optim Theory Appl

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In this paper, the exact minimax penalty function method is applied to solve constrained multiobjective optimization problems involving locally Lipschitz functions. The criteria for a saddle point for the original vector optimization problem are studied with the help of the penalized unconstrained vector optimization problem. Furthermore, we determine the conditions for which the (weak) efficient solutions of the vector optimization problem are equivalent to those of the associated, penalized unconstrained vector optimization problem. Some examples of nonsmooth multiobjective problems solved by using the exact minimax penalty method are presented to illustrate the results established in the paper.

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The exponential penalty function method for multiobjective programming problems

Cited by 16 publications

References 6 publications

Vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming Problems

Vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming Problems

Convergence of exponential penalty function method for multiobjective fractional programming problems

An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems

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