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.
The traditional approach in the solution of stochastic multiobjective programming problem involves transforming the original problem into a deterministic multiobjective programming problem. However, due to the complex...
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ISBN:
(纸本)9783319159348;9783319159331
The traditional approach in the solution of stochastic multiobjective programming problem involves transforming the original problem into a deterministic multiobjective programming problem. However, due to the complexity in practical application problems, the closed form of stochastic multiobjective programming problem is usually hard to obtain, and yet, there is surprisingly little literature that addresses this problem. The principal purpose of this paper is to propose a new hybrid algorithm to solve stochastic multiobjective programming problem efficiently, which is integrated with Latin Hypercube Sampling, Monte Carlo simulation, Support Vector Regression and Artificial Bee Colony algorithm. Several numerical examples are presented to illustrate the validity and performance of the hybrid algorithm. The results suggest that the proposed algorithm is very suitable for solving stochastic multiobjective programming problem.
Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be sufficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. D...
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Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be sufficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. Duality results are thus extended for a Wolfe-type or a Mond-Weir type dual.
In this paper, a class of more general generalized convex functions: (F, p)-invariantconvexity functions, are defined. On the basis of defintions, we have constructed generalduality models (VD); discussed duality prop...
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In this paper, a class of more general generalized convex functions: (F, p)-invariantconvexity functions, are defined. On the basis of defintions, we have constructed generalduality models (VD); discussed duality property of (VP) and (VD); proved weakly dualitytheorem, direct duality theorem and converse duality theorem.
In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are c...
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In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are convex. A sufficient condition for the connectedness of G-proper efficient solution set is established when objective functions are strictly quasiconvex.
In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, ...
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In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.
In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly c...
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In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly convex vector function, and the uniqueness of α major efficient solution when the objective function is weak strictly H α convex vector function.
This paper develops an interactive method, called flexible interaction multiobjective programming (FIMP), for solving multiobjective decision problems. In a decision process a minimax problem is iteratively solved wit...
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This paper develops an interactive method, called flexible interaction multiobjective programming (FIMP), for solving multiobjective decision problems. In a decision process a minimax problem is iteratively solved within a progressively reduced objective space until a noninferior solution which is preferred by the decision maker (DM) is found. The interaction process is easy, reliable and adaptive because (a) multiple possible choices of the contents and forms of expressing preference are provided to fit the needs of different situations; (b) the fuzziness or indecision of the DM’s preference can be handled; and (c) no quantitative judgement or quantitative information is required of the DM. The method is illustrated by a numerical example.
A new generalized class of higher-order (F, alpha, rho, d)-type I functions is introduced, and a general Mond-Weir type higher-order dual is formulated for a nondifferentiable multiobjective programming problem. Based...
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A new generalized class of higher-order (F, alpha, rho, d)-type I functions is introduced, and a general Mond-Weir type higher-order dual is formulated for a nondifferentiable multiobjective programming problem. Based on the concepts introduced, various higher-order duality results are established. At the end, some special cases are also discussed.
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