Research in optimization under uncertainty is alive. It assumes different shapes and forms, all concurring to the general goal of designing effective and efficient tools for handling imprecision in an Optimization set...
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Research in optimization under uncertainty is alive. It assumes different shapes and forms, all concurring to the general goal of designing effective and efficient tools for handling imprecision in an Optimization setting. In this paper we present a new approach for dealing with multiobjective programming problems with fuzzy objective functions. Similar to many approaches in the literature, our approach relies on the deffuzification of involved fuzzy quantities. Our improvement stem from the choice of a deffuzification operator that captures essential features of fuzzy parameters at hand rather than those that yield single values, leading to a loss of many useful information. Two oracles play a pivotal role in the proposed method. The first one returns a near interval approximation to a given fuzzy number. The other one delivers a Pareto Optimal solution of the resulting multiobjective program with interval coefficient. A numerical example is also provided for the sake of illustration.
A robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust opt...
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A robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust optimization is used in dealing with impreciseness while an interactive procedure is used in eliciting preference information from the decision maker and in making tradeoffs among the multiple objectives. Robust augmented weighted Tchebycheff programs are formulated from the multiobjective linear programming model using the concept of budget of uncertainty. A linear counterpart of the robust augmented weighted Tchebycheff program is derived. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs.
In this paper we establish an equivalence between the solutions of a generalized linear complementarity problem and efficient points of a related nonlinear (quadratic) multiobjective programming problem. An algorithm ...
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In this paper we establish an equivalence between the solutions of a generalized linear complementarity problem and efficient points of a related nonlinear (quadratic) multiobjective programming problem. An algorithm based on multiple objective programming approach is presented to solve generalized linear complementarity problem
In this paper we study second-order optimality conditions for the multi-objective programming problems with both inequality constraints and equality constraints. Two weak second-order constraint qualifications are int...
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In this paper we study second-order optimality conditions for the multi-objective programming problems with both inequality constraints and equality constraints. Two weak second-order constraint qualifications are introduced, and based on them we derive several second-order necessary conditions for a local weakly efficient solution. Two second-order sufficient conditions are also presented.
The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability...
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The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective programming problem under two perturbations are obtained in Banach space.
In the present article, we formulate two different kinds of higher-order dual models related to the multi-objective programming problem containing arbitrary norms. Furthermore, weak, strong and strict converse duality...
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In the present article, we formulate two different kinds of higher-order dual models related to the multi-objective programming problem containing arbitrary norms. Furthermore, weak, strong and strict converse duality results are established under the assumptions of higher-order ( Φ , ρ ) -invex function. Results obtained in this paper unify and extend some previously known results in the literature.
This paper presents the introduction of d-rho-(eta, theta)- univex functions, which are built upon the concepts of d-rho-(eta, theta)-invex functions and univex functions. By utilizing these concepts, the paper derive...
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This paper presents the introduction of d-rho-(eta, theta)- univex functions, which are built upon the concepts of d-rho-(eta, theta)-invex functions and univex functions. By utilizing these concepts, the paper derives various optimality results for feasible solutions to be considered as efficient or weak efficient solutions. Additionally, the paper establishes several duality theorems for Mond-Weir and Wolf duality.
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...
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In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective ***, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
The estimate of the parameters which define a conventional multiobjective decision making model is a difficult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses ...
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The estimate of the parameters which define a conventional multiobjective decision making model is a difficult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets and several fuzzy approaches to multiobjective programming have been developed [1,9-11]. The fuzziness of the parameters gives rise to a problem whose solution will also be fuzzy, see [2,3], and which is defined by its possibility distribution. Once the possibility distribution of the solution has been obtained, if the decision maker wants more precise information with respect to the decision vector, then we can pose and solve a new problem. In this case we try to find a decision vector, which approximates as much as possible the fuzzy objectives to the fuzzy solution previously obtained. In order to solve this problem we shall develop two different models from the initial solution and based on Goal programming: an Interval Goal programming Problem if we define the relation "as accurate as possible" based on the expected intervals of fuzzy numbers, as we showed in [4], and an ordinary Goal programming based on the expected values of the fuzzy numbers that defined the goals. Finally, we construct algorithms that implement the above mentioned solution method. Our approach will be illustrated by means of a numerical example. (C) 1999 Elsevier Science B.V. All rights reserved.
We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n-set functions.
We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n-set functions.
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