共查询到20条相似文献,搜索用时 639 毫秒
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We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the
scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we
recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison
among all three duals. Moreover, we show that their sets of maximal elements are equal. 相似文献
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S. J. Li X. K. Sun H. M. Liu S. F. Yao K. L. Teo 《Numerical Functional Analysis & Optimization》2013,34(1):65-82
In this article, under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are proposed for a constrained set-valued vector optimization problem. Weak duality, strong duality, and stability criteria are investigated. The inclusion relations between the image sets of the dual problems are also discussed. 相似文献
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We define weakly minimal elements of a set with respect to a convex cone by means of the quasi-interior of the cone and characterize them via linear scalarization, generalizing the classical weakly minimal elements from the literature. Then we attach to a general vector optimization problem, a dual vector optimization problem with respect to (generalized) weakly efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem, we derive vector dual problems with respect to weakly efficient solutions for both constrained and unconstrained vector optimization problems and the corresponding weak, strong and converse duality statements. 相似文献
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Gert Wanka 《Journal of Mathematical Analysis and Applications》2002,275(1):354-368
In this paper we present a duality approach for a multiobjective fractional programming problem. The components of the vector objective function are particular ratios involving the square of a convex function and a positive concave function. Applying the Fenchel-Rockafellar duality theory for a scalar optimization problem associated to the multiobjective primal, a dual problem is derived. This scalar dual problem is formulated in terms of conjugate functions and its structure gives an idea about how to construct a multiobjective dual problem in a natural way. Weak and strong duality assertions are presented. 相似文献
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In this paper, three kinds of conjugate dual problems are constructed by virtue of different perturbations to a constrained
vector optimization problem. Weak duality, strong duality, and some inclusion relations for the image sets of the three dual
problems are established.
This research was partially supported by the National Natural Science Foundation of China (Grant Number 60574073) and the
Natural Science Foundation Project of CQ CSTC (Grant Number 2007BB6117). The authors thank two anonymous referees for valuable
comments and suggestions, which helped improving the paper. 相似文献
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In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality. 相似文献
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G. Wanka 《Journal of Optimization Theory and Applications》2000,105(2):457-475
A general convex multiobjective control approximation problem is considered with respect to duality. The single objectives contain linear functionals and powers of norms as parts, measuring the distance between linear mappings of the control variable and the state variables. Moreover, linear inequality constraints are included. A dual problem is established, and weak and strong duality properties as well as necessary and sufficient optimality conditions are derived. Point-objective location problems and linear vector optimization problems turn out to be special cases of the problem investigated. Therefore, well-known duality results for linear vector optimization are obtained as special cases. 相似文献
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Duality for nonlinear multiple-criteria optimization problems 总被引:2,自引:0,他引:2
G. R. Bitran 《Journal of Optimization Theory and Applications》1981,35(3):367-401
In this paper, we develop a duality theory for nonlinear multiple-criteria optimization problems. The theory associates to efficient points a matrix, rather than a vector, of dual variables. We introduce a saddle-point dual problem, study stability concepts and Kuhn-Tucker conditions, and provide an economic interpretation of the dual matrix. The results are compared to the classical approach of deriving duality, by applying nonlinear programming duality theory to a problem obtained by conveniently weighting the criteria. Possible directions for future research are discussed.This work was performed under Grant No. MCS-77-24654, National Science Foundation.The author is grateful to Professors S. C. Graves and T. L. Magnanti, and two anonymous referees for helpful comments on an earlier version of this paper. 相似文献
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Wolfe Duality for Interval-Valued Optimization 总被引:1,自引:0,他引:1
H. C. Wu 《Journal of Optimization Theory and Applications》2008,138(3):497-509
Weak and strong duality theorems in interval-valued optimization problem based on the formulation of the Wolfe primal and
dual problems are derived. The solution concepts of the primal and dual problems are based on the concept of nondominated
solution employed in vector optimization problems. The concepts of no duality gap in the weak and strong sense are also introduced,
and strong duality theorems in the weak and strong sense are then derived. 相似文献
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《Optimization》2012,61(3):415-428
Abstract Lagrange duality theorems for vector and set optimization problems which are based on a consequent usage of infimum and supremum (in the sense of greatest lower and least upper bounds with respect to a partial ordering) have been recently proven. In this note, we provide an alternative proof of strong duality for such problems via suitable stability and subdifferential notions. In contrast to most of the related results in the literature, the space of dual variables is the same as in the scalar case, i.e. a dual variable is a vector rather than an operator. We point out that duality with operators is an easy consequence of duality with vectors as dual variables. 相似文献
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本文提出了一种整数规划中的指数一对数对偶.证明了此指数-对数对偶方法具有的渐近强对偶性质,并提出了不需要进行对偶搜索来解原整数规划问题的方法.特别地,当选取合适的参数和对偶变量时,原整数规划问题的解可以通过解一个非线性松弛问题来得到.对具有整系数目标函数及约束函数的多项式整规划问题,给出了参数及对偶变量的取法. 相似文献
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文章建立关于非可微凸规划的一个新的对偶问题,它不同于已知的对偶问题,文中证明了弱对偶性及强对偶性。并用Lagrange正则性证明了强对偶性的充要条件。最后,讨论了等式约束的情况。 相似文献
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《Optimization》2012,61(3):281-300
In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D 1), (D α) and (DFL ) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not. 相似文献
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On the relationship between fenchel and Lagrange duality for optimization problems in general spaces
《Optimization》2012,61(1):7-14
In this paper, the equivalence between a Fenchel and Lagrange duality theorem for optimization problems in dual pairs of real vector spaces is proved in a direct way. 相似文献
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In this article, gap functions for a generalized vector equilibrium problem (GVEP) with explicit constraints are investigated. Under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are investigated by considering the different perturbations to GVEP. Then, gap functions for GVEP are established by using the weak and strong duality results. As application, the proposed approach is applied to construct gap functions for a vector optimization problem and a generalized vector variational inequality problem. 相似文献
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Li-ping Pang Wei Wang Zun-quan Xia 《应用数学学报(英文版)》2006,22(1):49-58
The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven. 相似文献