In this paper, we discuss relations between a solution of a vector variational inequality problem with upper Dini directional derivatives or gradients and a properly efficient solution or an efficientsolution of a ve...
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In this paper, we discuss relations between a solution of a vector variational inequality problem with upper Dini directional derivatives or gradients and a properly efficient solution or an efficientsolution of a vector optimization problem. In particular, we give conditions under which equivalent relations between the two problems hold.
Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a pr...
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Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.
Recently Hachimi and Aghezzaf introduced the notion of (F,alpha,rho,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. Here, we extend the concepts of (F,alpha...
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Recently Hachimi and Aghezzaf introduced the notion of (F,alpha,rho,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. Here, we extend the concepts of (F,alpha,rho,d)-type I and generalized (F,alpha,rho, d)-type I functions to the continuous case and we use these concepts to establish various sufficient optimality conditions and mixed duality results for multiobjective variational problems. Our results apparently generalize a fairly large number of sufficient optimality conditions and duality results previously obtained for multiobjective variational problems.
In the paper, we introduce the concepts of -type I and generalized -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove ...
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In the paper, we introduce the concepts of -type I and generalized -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are -type I and/or generalized -type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) -type I objective and constraint functions.
In this paper, a class of multiobjective fractional programming problems (denoted by (MFP)) is considered. First, the concept of higher-order (F, alpha, rho, d)-convexity of a function f : C -> R with respect to th...
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In this paper, a class of multiobjective fractional programming problems (denoted by (MFP)) is considered. First, the concept of higher-order (F, alpha, rho, d)-convexity of a function f : C -> R with respect to the differentiable function phi : R-n x R-n -> R is introduced, where C is an open convex set in R-n and alpha : C x C -> R+ \ efficient is a positive value function. And an important property, which the ratio of higher-order ( F, alpha, rho, d)-convex functions is also higher-order (F', alpha', rho', d')-convex, is proved. Under the higher-order (F, alpha, rho, d)-convexity assumptions, an alternative theorem is also given. Then, some sufficient conditions characterizing properly (or weakly) efficientsolutions of (MFP) are obtained from the above property and alternative theorem. Finally, a class of dual problems is formulated and appropriate duality theorems are proved.
For a given multi-objective optimization problem, we introduce and study the notion of alpha-proper efficiency. We give two characterizations of such proper efficiency: one is in terms of exact penalization and the ot...
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For a given multi-objective optimization problem, we introduce and study the notion of alpha-proper efficiency. We give two characterizations of such proper efficiency: one is in terms of exact penalization and the other is in terms of stability of associated parametric problems. Applying the aforementioned characterizations and recent results on global error bounds for inequality systems, we obtain verifiable conditions for alpha-proper efficiency. For a large class of polynomial multi-objective optimization problems, we show that any efficientsolution is alpha-properlyefficient under some mild conditions. For a convex quadratically constrained multi-objective optimization problem with convex quadratic objective functions, we show that any efficientsolution is alpha-properlyefficient with a known estimate on alpha whenever its constraint set is bounded. Finally, we illustrate our achieved results with examples, and give an example to show that such an enhanced efficiency property may not hold for multi-objective optimization problems involving C (a)-functions as objective functions.
We extend the concepts of B-type I and generalized B-type I functions to the continuous case and we use these concepts to establish sufficient optimality conditions and duality results for multiobjective variational p...
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We extend the concepts of B-type I and generalized B-type I functions to the continuous case and we use these concepts to establish sufficient optimality conditions and duality results for multiobjective variational programming problems. (C) 1999 Academic Press.
A class of BF-type I functions and its extensions are introduced in the continuous case, an example is presented in support. Utilizing these new concepts, sufficient optimality conditions and duality results are prese...
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A class of BF-type I functions and its extensions are introduced in the continuous case, an example is presented in support. Utilizing these new concepts, sufficient optimality conditions and duality results are presented for multiobjective variational problems involving arbitrary norms. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, we establish relations between a solution of a vector continuous-time program and a solution of a vector variational-type inequality problem with functionals.
In this paper, we establish relations between a solution of a vector continuous-time program and a solution of a vector variational-type inequality problem with functionals.
In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar...
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In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properlyefficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.
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