In this paper by employing an asymptotic approach we develop an existence and stability theory for convex multiobjective programming. We deal with the set of weakly efficient minimizers. To this end we employ a notion...
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In this paper by employing an asymptotic approach we develop an existence and stability theory for convex multiobjective programming. We deal with the set of weakly efficient minimizers. To this end we employ a notion of convergence for vector-valued functions close to that due to Lemaire. (c) 2008 Elsevier B.V. All rights reserved.
Certain omissions have been pointed out in some papers on symmetric duality in multiobjective programming. Corrective measures have also been discussed. (C) 2009 Elsevier Inc. All rights reserved.
Certain omissions have been pointed out in some papers on symmetric duality in multiobjective programming. Corrective measures have also been discussed. (C) 2009 Elsevier Inc. All rights reserved.
In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A cou...
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In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A counterexample has been furnished which shows that the convexity assumption cannot be extended to include the quasiconvexity case. The second theorem on sufficiency requires the strict pseudoconvexity of the functions involved.
In this paper,we point out some deficiencies in a recent paper(Lee and Kim in *** Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-...
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In this paper,we point out some deficiencies in a recent paper(Lee and Kim in *** Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.
We consider non-smooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several optimality conditions under various (generalized) V-invexity assumptio...
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We consider non-smooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several optimality conditions under various (generalized) V-invexity assumptions and certain regularity conditions are presented. Further, we introduce a Mond-Weir type dual and establish duality relations under the aforesaid assumptions.
We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several co...
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We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given in such a way that they generalize the classical ones, when the functions are differentiable. The relationships between them are analyzed. Then, we establish strong Kuhn-Tucker necessary optimality conditions in terms of the Clarke subdifferentials such that the multipliers of the objective function are all positive. Furthermore, sufficient optimality conditions under generalized convexity assumptions are derived. Moreover, the concept of efficiency is used to formulate duality for nonsmooth multiobjective problems. Wolf and Mond-Weir type dual problems are formulated. We also establish the weak and strong duality theorems.
Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely ...
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Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely used concept of efficiency has to be redefined for these problems. The use of interactive procedures can somehow ease this complexity, allowing the decision maker to learn about the problem itself, and to look for his most preferred solution. Reference point schemes can be adapted to stochastic problem, by asking the decision maker to provide, not only desirable levels for the objectives, but also the desired probability to achieve these values. In this paper, we analyze the different kinds of achievement scalarizing functions that can be used in this environment, and we study the efficiency (in the stochastic sense) of the different solutions obtained. As a result, a synchronous interactive method is proposed for a class of stochastic multiobjective problems, where only the objective functions are random. Several solutions can be generated by this new method, making use of the same preferential information, using the different achievement scalarizing functions. The preferential information (levels and probabilities for the objectives) is incorporated into the achievement scalarizing functions in a novel way to generate the new solutions. The special case of linear normal problems is addressed separately. The performance of the algorithm is illustrated with a numerical example.
In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized ...
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In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of this method is established. Further, the exactness property of a vector exact penalty function method is defined and analyzed in the context of the introduced vector exponential penalty function method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential penalty function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving functions are r-invex.
Environmental management problems are very complex and require considering numerous factors, such as environmental, economic, and social aspects. Qualitative and quantitative data always exist simultaneously in real w...
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Environmental management problems are very complex and require considering numerous factors, such as environmental, economic, and social aspects. Qualitative and quantitative data always exist simultaneously in real world decision-making situations. A novel multiobjective programming approach is proposed in this study to solve qualitative and quantitative objectives for environmental management problems. This approach integrates the multiattribute and multiobjective decision-making methods and contains three main steps to solve the multiobjective programming problems, including formulation of the decision model, the alternatives prioritization by the fuzzy AHP method, and solving the model. A case study of food waste management conducted in Taiwan is used to demonstrate the practicality of this approach. (c) 2005 Elsevier B.V. All rights reserved.
In this note we present a new multiplier rule for a constrained multiobjective programming problem with continuous data by using the concept of unbounded approximate Jacobians recently developed by Jeyakumar and Luc [...
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In this note we present a new multiplier rule for a constrained multiobjective programming problem with continuous data by using the concept of unbounded approximate Jacobians recently developed by Jeyakumar and Luc [SIAM J. Control Optim., 36 ( 1998), pp. 1815 1832].
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