In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give *** optimality conditions of the nonsmooth generalized convex multi-objective progra...
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In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give *** optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone *** solution.
New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebr...
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New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.
A class of multiobjective fractional programming problems is considered and duality results are established in terms of properly efficient solutions of the primal and dual programs. Further a vector-valued ratio type ...
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A class of multiobjective fractional programming problems is considered and duality results are established in terms of properly efficient solutions of the primal and dual programs. Further a vector-valued ratio type Lagrangian is introduced and certain vector saddlepoint results are presented.
MOPEN is a computational package designed as a global tool for Linear multiobjective and Goal programming problems with continuous and/or integer variables. The main existing techniques for these problems have been in...
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MOPEN is a computational package designed as a global tool for Linear multiobjective and Goal programming problems with continuous and/or integer variables. The main existing techniques for these problems have been included in this package. That is, it is possible to generate or approximate the efficient set using Generating Methods, to obtain Compromise solutions or to use Goal programming or reference Point approaches. As will be described, many advanced options have been implemented with every method. MOPEN has been implemented under a Windows environment;thus, it is easy to build and handle the data entry files and the result layout files. The behavior of MOPEN-in terms of CPU time used to solve large problems-can be considered as good;therefore, this package is a powerful tool to handle the previously mentioned problems. (c) 2004 Elsevier B.V. All rights reserved.
We consider some types of generalized convexity and discuss duality results for a fractional programming problem involving (F, b, phi, rho, theta)-univex n-set functions. Almost all results presented until now in the ...
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We consider some types of generalized convexity and discuss duality results for a fractional programming problem involving (F, b, phi, rho, theta)-univex n-set functions. Almost all results presented until now in the literature were obtained under the assumption that the function F is sublinear or, in the last time, convex in the third argument. In our approach, we suppose that F is a quasiconvex function in the third argument. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper, a 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. A ...
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In this paper, a 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. A new class of higher order (F, alpha, rho, d)-type I function is introduced. Necessary optimality conditions and the duality theorems for Wolfe and unified higher order dual problems are established. Several known results can be deduced as special cases.
In this paper,based on the fuzzy random theory, the fuzzy random multiobjective programming(FR-MOP) problems are *** first investigate the expected value model,and study its *** on the proposed model,the expected-valu...
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In this paper,based on the fuzzy random theory, the fuzzy random multiobjective programming(FR-MOP) problems are *** first investigate the expected value model,and study its *** on the proposed model,the expected-value efficient solution and the expected-value weakly efficient solution are defined. To solve the FRMOP problems,a method,called method of main objective function,is presented,whose results can provide theoretical foundation for designing solution ***,a numerical example are given to explain the solution method.
Consider a system of nondifferentiable multiobjective nonlinear fractional programming problem involving exponential (p, r)-invex functions with respect to.. A new concept of saddle point for a mixed Lagrange function...
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Consider a system of nondifferentiable multiobjective nonlinear fractional programming problem involving exponential (p, r)-invex functions with respect to.. A new concept of saddle point for a mixed Lagrange function is introduced. We establish the equivalence between the saddle point and an efficient solution of the minimizationmultiobjective fractional problem involving exponential (p, r)-invexity assumptions.
We consider the proximal point method for solving unconstrained multiobjective programming problems including two families of real convex functions, one of them defined on the positive orthant and used for modifying a...
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We consider the proximal point method for solving unconstrained multiobjective programming problems including two families of real convex functions, one of them defined on the positive orthant and used for modifying a variant of the logarithm-quadratic regularization introduced recently and the other for defining a family of scalar representations based on 0-coercive convex functions. We show convergent results, in particular, each limit point of the sequence generated by the method is a weak Pareto solution. Numerical results over fourteen test problems are shown, some of them with complicated pareto sets.
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