In this paper, optimality for multiobjective programming problems having invex objective and constraint functions (with respect to the same function eta) is considered. An equivalent vector programming problem is cons...
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In this paper, optimality for multiobjective programming problems having invex objective and constraint functions (with respect to the same function eta) is considered. An equivalent vector programming problem is constructed by a modification of the objective function. Furthermore, an eta-Lagrange function is introduced for a constructed multiobjective problem and modified saddle point results are presented.
Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be a...
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Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of a we get different alpha-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper. (C) 2013 Elsevier Inc. All rights reserved.
In multiobjective programming, the concept of equitable efficiency strengthens the concept of Pareto efficiency by additionally requiring that the objective functions be anonymous and satisfy the principle of transfer...
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In multiobjective programming, the concept of equitable efficiency strengthens the concept of Pareto efficiency by additionally requiring that the objective functions be anonymous and satisfy the principle of transfers. The preference relation satisfying these assumptions is not related to a cone as is the Pareto preference. A complete preference structure of equitability is derived and an approach to generating equitably efficient solutions is proposed. (c) 2006 Elsevier Ltd. All rights reserved.
In this paper, new classes of generalized (F,alpha,rho,d)-V-type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality ...
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In this paper, new classes of generalized (F,alpha,rho,d)-V-type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.
In this paper a new class of second-order (F, alpha, p, d)-V-type I functions is introduced that generalizes the notion of (F, alpha, p, theta)-V-convex functions introduced by Zalmai (Computers Math. Appl. 2002;43:14...
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In this paper a new class of second-order (F, alpha, p, d)-V-type I functions is introduced that generalizes the notion of (F, alpha, p, theta)-V-convex functions introduced by Zalmai (Computers Math. Appl. 2002;43:1489-1520) and (F, alpha, p, p, d)-type I functions defined by Hachimi and Aghezzaf (Numer. Funct. Anal. Optim. 2004, 25:725-736). Based on these functions, weak, strong, and strict converse duality theorems are derived for Wolfe and Mond-Weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems.
In this paper, a generalization of convexity, namely (p,r)-invexity, is considered in the case of nonlinear multi-objective programming problems where the functions involved are differentiable. The assumptions on Pare...
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In this paper, a generalization of convexity, namely (p,r)-invexity, is considered in the case of nonlinear multi-objective programming problems where the functions involved are differentiable. The assumptions on Pareto solutions are relaxed by means of (p, r)-invex functions. Also some duality results are obtained for such optimization problems. (C) 2002 Elsevier B.V. All rights reserved.
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 w...
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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.
In this paper, we are concerned with the nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized d-type-I functions. By utilizing the new concepts...
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In this paper, we are concerned with the nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized d-type-I functions. By utilizing the new concepts, Antczak type Karush-Kuhn-Tucker sufficient optimality conditions, Mond-Weir type and general Mond-Weir type duality results are obtained for nondifferentiable and multiobjective programming.
This paper is devoted to the study of nonsmooth multiobjective semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite. We introduce several k...
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This paper is devoted to the study of nonsmooth multiobjective semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite. We introduce several kinds of constraint qualifications for these problems, and then necessary optimality conditions for weakly efficient solutions are investigated. Finally by imposing assumptions of generalized convexity we give sufficient conditions for efficient solutions.
In this paper, we introduce new classes of functions called d-V-type-I univex by extending the definition of d-V-type-I functions and consider a multiobjective optimization problem involving generalized d-V-type-I uni...
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In this paper, we introduce new classes of functions called d-V-type-I univex by extending the definition of d-V-type-I functions and consider a multiobjective optimization problem involving generalized d-V-type-I univex functions. A number of Karush-Kuhn-Tucker-type sufficient optimality conditions are obtained for a feasible solution to be a weak Pareto efficient solution. The Mond-Weir-type duality results are also presented. The results obtained in this paper generalize and extend the previously known result in this area. (C) 2008 Elsevier B.V. All rights reserved.
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