Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is prov...
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Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is proved. In addition, the approach is applied to solving a finite min-max MOPP.
In this papert the theory of major efficiency for multiobjective programmingis *** major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions...
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In this papert the theory of major efficiency for multiobjective programmingis *** major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.
Many important achievement of multiobjective programming are all based on convex programming. How to extend and deepen them, one vital aspect is extend the. convexity functions which are refered in various sense to mo...
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ISBN:
(纸本)9787560322780
Many important achievement of multiobjective programming are all based on convex programming. How to extend and deepen them, one vital aspect is extend the. convexity functions which are refered in various sense to more general convexity functions. In this paper, a class of generalized convexity fuctions: (F, rho)-invariant convex function, (F, rho)- invariant quasiconvex function, (F, rho)-invariant pseudoconvex function and (F, rho)-strictly invariant pseudoconvex. function are defined. On the basis of definitions, we have constructed general duality models (VD);discussed duality property of (VP) and (VD);proved weakly duality theorem, direct duality theorem and converse duality theorem. The functions of a class of generalized convexity are extension of the several different generalized convexity functions presented in the references [1], [2], [3], [4] and [5]. The results of this paper can be thought of as improved extended and generalized of the main results of the references 111-1101.
Necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and th...
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Necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and then using known results in convex programming.
In the paper two theorems are given concerning the relationship between the conflict among the objectives and the nature of the Pareto-set in vector optimization. Taking this into consideration, a method is developed ...
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The concepts of (Φ, ρ)-invexity have been given by Caristi, Ferrara and Stefanescu[32]. We consider a higher-order dual model associated to a multiobjective programming problem involving support functions and a weak...
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The concepts of (Φ, ρ)-invexity have been given by Caristi, Ferrara and Stefanescu[32]. We consider a higher-order dual model associated to a multiobjective programming problem involving support functions and a weak duality result is established under appropriate higher-order (Φ, ρ)-invexity conditions.
Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is prov...
详细信息
Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is proved. In addition, the approach is applied to solving a finite min-max MOPP.
The purpose of this paper is to establish characterizations for efficient solutions to multiobjective programming problems. We extend the concept of G-Karush-Kuhn-Tucker problems to the multiobjective programming case...
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ISBN:
(纸本)9781467347143
The purpose of this paper is to establish characterizations for efficient solutions to multiobjective programming problems. We extend the concept of G-Karush-Kuhn-Tucker problems to the multiobjective programming case and introduce a new class of multiobjective programming problems, which is called G-KKT-pseudoinvex multiobjective programming problems. We show that the G-Karush-Kuhn-Tucker points to be efficient solutions, if and only if the multiobjective programming problem is G-KKT-pseudoinvex. Similarly, we also propose characterizations for efficient solutions by using G-Fritz-John optimality conditions. We establish an example in support of our investigation.
The purpose of this paper is concerned with a class of multi objective programming problems in which the objective functions and constrained functions are twice differentiable and containing the support functions of a...
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The purpose of this paper is concerned with a class of multi objective programming problems in which the objective functions and constrained functions are twice differentiable and containing the support functions of a compact convex set. For such mathematic programming, to deal with its dual problem, first, the concept of second order B - (p, r) - invexity is introduced. Further, the Mangasarian type second order dual model associated with the multi objective problem are formulated. Several weak, strong and strict converse dual theorems are established and proved by utilizing the new generalized convexity. The results extend and improve the corresponding results in the literature.
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak ...
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In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush-Kuhn-Tucker sufficient optimality condition and establish Mond-Weir type and general Mond-Weir type duality results for the nondifferentiable multiobjective programming problem. (C) 2003 Elsevier B.V. All rights reserved.
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