We use normal directions of the outcome set to develop a method of outer approximation for solving generalized convex multiobjective programming problems. We prove the convergence of the method and report some computa...
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We use normal directions of the outcome set to develop a method of outer approximation for solving generalized convex multiobjective programming problems. We prove the convergence of the method and report some computational experiments. As an application, we obtain an algorithm to solve an associated multiplicative problem over a convex constraint set.
In this paper we assume that a deterministic multiobjective programming problem is approximated by surrogate problems based on estimations for the objective functions and the constraints. Making use of a large deviati...
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In this paper we assume that a deterministic multiobjective programming problem is approximated by surrogate problems based on estimations for the objective functions and the constraints. Making use of a large deviations approach, we investigate the behaviour of the constraint sets, the sets of efficient points and the solution sets if the size of the underlying sample tends to infinity. The results are illustrated by applying them to stochastic programming with chance constraints, where (i) the distribution function of the random variable is estimated by the empirical distribution function, (ii) certain parameters have to be estimated.
In recent years portfolio optimization models that consider more criteria than the expected return and variance objectives of the Markowitz model have become popular. These models are harder to solve than the quadrati...
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In recent years portfolio optimization models that consider more criteria than the expected return and variance objectives of the Markowitz model have become popular. These models are harder to solve than the quadratic mean-variance problem. Two approaches to find a suitable portfolio for an investor are possible. In the multiattribute utility theory (MAUT) approach a utility function is constructed based on the investor's preferences and an optimization problem is solved to find a portfolio that maximizes the utility function. In the multiobjective programming (MOP) approach a set of efficient portfolios is computed by optimizing a scalarized objective function. The investor then chooses a portfolio from the efficient set according to his/her preferences. We outline these two approaches using the UTADIS method to construct a utility function and present numerical results for an example.
In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et ...
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In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et al. Higher order duality in inultiobjective programming with cone constraints. Optimization, 2010, 59： 29-43].
Designing water quality management strategies is often complicated by the difficulty in simultaneously considering large amounts of relevant data, applicable submodels, competing objectives, unquantifiable factors, no...
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Designing water quality management strategies is often complicated by the difficulty in simultaneously considering large amounts of relevant data, applicable submodels, competing objectives, unquantifiable factors, nonlinear characteristics, and uncertainty during parameterization. Mathematical optimization techniques offer promise in identifying optimal or satisfactory strategies that may be used as benchmarks for decision making. Newer optimization techniques such as genetic algorithm (GA) and fuzzy mathematical programming make the search for optimal control strategies in an uncertain environment more feasible. Using a probabilistic search procedure that emulates Darwinian natural selection, GAs allow multicriteria decision making with respect to both nonlinear feature and fuzzy characteristics to be incorporated directly into the optimization process and generate trade-off curves between cost and environmental quality while identifying good control strategies. This paper verifies such a discovery by a case study of water quality control in the Tseng-Wen river basin in Taiwan. (C) 1998 IAWQ. Published by Elsevier Science Ltd.
We establish a Lagrange multiplier rule, in terms of Clarke generalized gradient, that characterizes epsilon-efficiency of a nondifferentiable multiobjective programming problem on a real Banach space. This rule is th...
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We establish a Lagrange multiplier rule, in terms of Clarke generalized gradient, that characterizes epsilon-efficiency of a nondifferentiable multiobjective programming problem on a real Banach space. This rule is then utilized to establish relationship between epsilon-efficient solution of multiobjective program and generalized saddle point of an appropriate vector-valued Lagrangian under invexity hypothesis. (C) 2003 Elsevier B.V. All rights reserved.
In this paper, a class of nonsmooth multiobjective programming problems with inequality constraints is considered. We introduce the concepts of V-r-pseudo-invex, strictly V-r-pseudo-invex and V-r-quasi-invex functions...
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In this paper, a class of nonsmooth multiobjective programming problems with inequality constraints is considered. We introduce the concepts of V-r-pseudo-invex, strictly V-r-pseudo-invex and V-r-quasi-invex functions, in which the involved functions are locally Lipschitz. Based upon these generalized V-r-invex functions, sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived. Appropriate duality theorems are proved for a Mond-Weir-type dual program of a nonsmooth multiobjective programming under the aforesaid functions. (C) 2011 Elsevier Ltd. All rights reserved.
Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. ...
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Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers more than 50 articles published since 1975.
In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modi...
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In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-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 a saddle point are given.
In this study, an alternative theorem for the subconvexlike mapping in topological vector space is established. With this alternative theorem as an aid, the generalized Fritz John conditions and the generalized Kuhn-T...
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In this study, an alternative theorem for the subconvexlike mapping in topological vector space is established. With this alternative theorem as an aid, the generalized Fritz John conditions and the generalized Kuhn-Tucker conditions in terms of Gateaux derivatives of multiobjective programming problem in the ordered topological vector space are given. (C) 2003 Elsevier Inc. All rights reserved.
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