In this work, a pair of higher-order symmetric dual multiobjective optimization problems is formulated. Weak, strong and converse duality theorems are established under suitable assumptions. Some examples are also giv...
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In this work, a pair of higher-order symmetric dual multiobjective optimization problems is formulated. Weak, strong and converse duality theorems are established under suitable assumptions. Some examples are also given to illustrate our main results. Furthermore, certain deficiencies in the formulations and the proof of the work of Kassem [Applied Mathematics and Computation, 209 (2009), 405-409] are pointed out.
In this paper, sufficient conditions for superstrict minima of order m to nondifferentiable multiobjective optimization problems with an arbitrary feasible set are provided. These conditions are expressed through the ...
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In this paper, sufficient conditions for superstrict minima of order m to nondifferentiable multiobjective optimization problems with an arbitrary feasible set are provided. These conditions are expressed through the Studniarski derivative of higher order. If the objective function is Hadamard differentiable, a characterization for strict minimality of order 1 (which coincides with superstrict minimality in this case) is obtained.
Necessary Kuhn-Tucker conditions up to precision epsilon without constraint qualification for epsilon-Pareto optimality of multiobjective programming are derived. This article suggests the establishment of a Wolfe-typ...
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Necessary Kuhn-Tucker conditions up to precision epsilon without constraint qualification for epsilon-Pareto optimality of multiobjective programming are derived. This article suggests the establishment of a Wolfe-type epsilon-duality theorem for nondifferentiable, nonconvex, multi-objective minimization problems. The epsilon-vector Lagrangian and the generalized epsilon-saddle point for Pareto optimality are studied.
In this paper, we consider a generalization of convexity for nonsmooth multiobjective programming problems. We obtain sufficient optimality conditions under generalized (F rho)-convexity.
In this paper, we consider a generalization of convexity for nonsmooth multiobjective programming problems. We obtain sufficient optimality conditions under generalized (F rho)-convexity.
To remedy challenges resulting from a high number of objectives in multiobjective programming and multicriteria decision making, this paper chooses to decompose the vector objective function and characterizes the rela...
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To remedy challenges resulting from a high number of objectives in multiobjective programming and multicriteria decision making, this paper chooses to decompose the vector objective function and characterizes the relationships between solutions for the original problem and the collection of decomposed subproblems. In particular, it is shown how solutions that are found using this decomposition approach relate to solutions found by traditional scalarization techniques. For the selection of a final solution, two interactive coordination methods are proposed that allow to find any solution for the original problem by merely solving the smaller-sized subproblems, while integrating both preferences of the decision maker and trade-off information obtained from a sensitivity analysis. A theoretical foundation for the procedures is established, and their application is illustrated for portfolio optimization and a design selection problem.
In this paper, cone-second order pseudo-invex and strongly cone-second order pseudo-invex functions are defined. A pair of Mond-Weir type second order symmetric dual multiobjective programs is formulated over *arbitra...
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In this paper, cone-second order pseudo-invex and strongly cone-second order pseudo-invex functions are defined. A pair of Mond-Weir type second order symmetric dual multiobjective programs is formulated over *arbitrary cones. Weak, strong and converse duality theorems are established under aforesaid generalized invexity assumptions. A second self-duality theorem is also given by assuming the functions involved to be skew-symmetric. (c) 2006 Elsevier B.V. All rights reserved.
This paper proposes a crisp two-objective logarithmic programming model to help companies decide their advertising campaigns on TV networks for mature products. Both objectives are: (a) to achieve the highest audience...
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This paper proposes a crisp two-objective logarithmic programming model to help companies decide their advertising campaigns on TV networks for mature products. Both objectives are: (a) to achieve the highest audience impact and (b) to reduce advertising costs as much as possible. Information input is fuzzily elaborated from statistical data, the fuzzy variables being defuzzified to introduce them into the crisp model. This fuzzy information is elicited by TV experts (often independent consultants). Although these experts know statistical information on audience in the past, they do not fully trust its predictive ability. The approach leads to the strategic advertisement (ad) placement among different broadcasts. Users (often managers of big companies) should inform the analyst about their advertising campaign budget. From Weber and Fechner-based psychological research, the ad impact during the advertising campaign is measured depending on the logarithm of ad repetitions. The crisp two-objective problem is solved by a tradeoff method subject to TV technical constraints. A case study with real world data is developed. (C) 2009 Elsevier Ltd. All rights reserved
In this paper, for finding a minimal efficient solution of nonconvex multiobjective programming, a constraint shifting combined homotopy is constructed and the global convergence is obtained under some mild conditions...
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In this paper, for finding a minimal efficient solution of nonconvex multiobjective programming, a constraint shifting combined homotopy is constructed and the global convergence is obtained under some mild conditions. The method requires that the initial point needs to be only in the shifted feasible set not necessarily in the original feasible set, and the normal cone condition need only be satisfied in the boundary of the shifted feasible set not the original constraint set. Some numerical tests are done and made comparison with a combined homotopy interior point method. The results show that our method is feasible and effective.
In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond-Wei...
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In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond-Weir and general Mond-Weir type duality under the above generalized type I assumptions.
In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objecti...
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In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of wr- equitable efficiency, where w ∈ R＋ m is a weight vector. First some theoretical and practical aspects of Pwr- equitably efficient solutions are discussed and by using the concept of Pwr-equitable efficiency one model is presented to coordinate weakly wr-equitable efficient solutions of subproblems. Then the concept of Pw ∞- equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.
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