We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity a...
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We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity assumptions and certain regularity conditions are presented. In addition, we introduce a Wolfe-type dual and Mond-Weir-type dual and establish duality relations under various (generalized) invexity and regularity conditions.
In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferen...
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In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results.
The purpose of this paper is to present some results about the convergence of interactive reference point methods in multiobjective programming. In particular, we describe how dual information may guide the decision m...
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The purpose of this paper is to present some results about the convergence of interactive reference point methods in multiobjective programming. In particular, we describe how dual information may guide the decision maker in his choice of the successive reference points. In the literature different convergence models have been proposed. The analyst may induce convergence by selecting appropriate rules of the communication. Or he may rely on the learning process of the decision maker to induce some kind of ‘psychological’ convergence. In neither case are the activities of the decision maker precisely described. Consequently, the quality of the final decision cannot be established, and the question of convergence remains an unsolved issue. We describe different ways in which the decision maker may select his successive reference points, and we discuss the convergence of the resulting reference point procedures. Also, we comment on the relevance of these different assumptions about the decision maker's behavior. The procedures are illustrated by a small numerical example. [ABSTRACT FROM AUTHOR]
In this paper, we give an application of UV-decomposition method of convex programming to multiobjective programming, and offer a new algorithm for solving semi-infinite multiobjective programming. Finally, the superl...
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In this paper, we give an application of UV-decomposition method of convex programming to multiobjective programming, and offer a new algorithm for solving semi-infinite multiobjective programming. Finally, the superlinear convergence of the algorithm is proved.
multiobjective programming, a technique for solving mathematical optimization problems with multiple conflicting objectives, has received increasing attention among researchers in various academic disciplines. A summa...
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multiobjective programming, a technique for solving mathematical optimization problems with multiple conflicting objectives, has received increasing attention among researchers in various academic disciplines. A summary of multiobjective programming techniques and a review of their applications in quantitative psychology are provided. (C) 2011 Elsevier Inc. All rights reserved.
In this paper, we propose an interactive method for multiobjective linear programming problems, in which fuzzy coefficients, random variable coefficients and fuzzy random variable coefficients are involved in the obje...
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In this paper, we propose an interactive method for multiobjective linear programming problems, in which fuzzy coefficients, random variable coefficients and fuzzy random variable coefficients are involved in the objective functions respectively. In the proposed method, it is assumed that the decision maker has a fuzzy goal for each objective function, and such a fuzzy goal can be quantified by eliciting the membership function. Through a possibility measure and a fractile optimization model, the original problem is transformed to the well-defined multiobjective programming problem. Then, a generalized Pareto optimal concept is defined, and an interactive algorithm is proposed to obtain a satisfactory solution from among a generalized Pareto optimal solution set.
A methodology is presented to explore the tradeoffs associated with the numerous solutions typically obtained through multiobjective optimization procedures. The method is a graphical surface navigation technique base...
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A methodology is presented to explore the tradeoffs associated with the numerous solutions typically obtained through multiobjective optimization procedures. The method is a graphical surface navigation technique based on a spring equilibrium analogy. The procedure is cast in the framework of an interactive graphical session, which permits a user easily to move from one noninferior point to another on the objective response surface. A zooming capability is also incorporated which facilitates refinement of the noninferior set approximation over particular areas of interest and as well, provides for the capability to examine the exact noninferior set. A three-dimensional and a five-dimensional problem are used to illustrate the method.
Necessary and sufficient conditions of Fritz John type for Pareto optimality of multiobjective programming problems are derived. This article suggests to establish a Wolfe-type duality theorem for nonlinear, nondiffer...
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Necessary and sufficient conditions of Fritz John type for Pareto optimality of multiobjective programming problems are derived. This article suggests to establish a Wolfe-type duality theorem for nonlinear, nondifferentiable, convex multiobjective minimization problems. The vector Lagrangian and the generalized saddle point for Pareto optimality are studied. Some previously known results are shown to be special cases of the results described in this paper.
This study examines new versions of two interactive methods to address multiobjective problems, the aim of which is to enable the decision maker to reach a solution within the range of those considered efficient in a ...
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This study examines new versions of two interactive methods to address multiobjective problems, the aim of which is to enable the decision maker to reach a solution within the range of those considered efficient in a portfolio selection model, in which several objectives are pursued concerning risk and return and given that these are clearly conflicting objectives, the profile of the model proposed is multicriteria. Normally the range of efficient portfolios is fairly extensive thus making the selection of a single one an onerous task. In order to facilitate this process, interactive methods are used aimed at guiding the decision maker towards the optimal solution based on his preferences. Several adaptations were carried out on the original methods in order to facilitate the interactive process, improving the quality of the obtained portfolios, and these were applied to data obtained from the Madrid Stock Market, interaction taking place with two decision makers, one of whom was more aggressive than the other in their selections made.
In this article, new classes of generalized invex functions, called second-order B - (p, r) - V - type I functions, is intuoduced. The new functions include many well-known classes of generalized invex functions as it...
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In this article, new classes of generalized invex functions, called second-order B - (p, r) - V - type I functions, is intuoduced. The new functions include many well-known classes of generalized invex functions as its subclasses. Further, a class of nondifferentiable multiobjective programming problem is considered where every component of objective and constraint functions contain a term involving the support function of a compact convex set. Based upon the new generalized invexity assumption in the functions involved, several KKT sufficient conditions for weakly eff icient solutions and efficient solutions of the multiobjective programming problem are established and proved. This paper will extend notions of convexity and larger the classes of optimization problems.
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