共查询到10条相似文献,搜索用时 281 毫秒
1.
Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps 总被引:34,自引:0,他引:34
This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained 相似文献
2.
In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdifferentials and zero-like functions.The authors greatly appreciate helpful and valuable comments and suggestions received from the referee. 相似文献
3.
Vsevolod I. Ivanov 《Optimization Letters》2012,6(1):43-54
In this paper we define two notions: Kuhn–Tucker saddle point invex problem with inequality constraints and Mond–Weir weak
duality invex one. We prove that a problem is Kuhn–Tucker saddle point invex if and only if every point, which satisfies Kuhn–Tucker
optimality conditions forms together with the respective Lagrange multiplier a saddle point of the Lagrange function. We prove
that a problem is Mond–Weir weak duality invex if and only if weak duality holds between the problem and its Mond–Weir dual
one. Additionally, we obtain necessary and sufficient conditions, which ensure that strong duality holds between the problem
with inequality constraints and its Wolfe dual. Connections with previously defined invexity notions are discussed. 相似文献
4.
Aparna Mehra 《Journal of Mathematical Analysis and Applications》2002,276(2):815-832
In this paper, we establish a scalarization theorem and a Lagrange multiplier theorem for super efficiency in vector optimization problem involving nearly convexlike set-valued maps. A dual is proposed and duality results are obtained in terms of super efficient solutions. A new type of saddle point, called super saddle point, of an appropriate set-valued Lagrangian map is introduced and is used to characterize super efficiency. 相似文献
5.
In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm. 相似文献
6.
In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm. 相似文献
7.
本文讨论无限维向量最优化问题的Lagrange对偶与弱对偶,建立了若干鞍点定理与弱鞍点定理.作为研究对偶问题的工具,建立了一个新的择一定理. 相似文献
8.
J. C. Pomerol 《Journal of Optimization Theory and Applications》1982,38(3):307-317
We prove that, under the usual constraint qualification and a stability assumption, the generalized gradient set of the marginal function of a differentiable program in a Banach space contains the Lagrange multiplier set. From there, we deduce a sufficient condition in order that, in finite-dimensional spaces, the Lagrange multiplier set be equal to the generalized gradient set of the marginal function.The author wishes to thank J. B. Hiriart-Urruty for many helpful suggestions during the preparation of this paper. He also wishes to express his appreciation to the referees for their many valuable comments. 相似文献
9.
P. H. Sach 《Journal of Global Optimization》2006,35(1):1-25
In this paper we give necessary conditions for Hartley proper efficiency in a vector optimization problem whose objectives
and constraints are described by nonconvex locally Lipchitz set-valued maps. The obtained necessary conditions are written
in terms of a Lagrange multiplier rule. Our approach is based on a reduction theorem which leads the problem of studying proper
efficiency to a scalar optimization problem whose objective is given by a function of max-type. Sufficient conditions for
Hartley proper efficiency are also considered. 相似文献
10.
集—集映射向量极值问题的Lagrange乘子和鞍点定理 总被引:1,自引:1,他引:0
本文先建立了集-集映射的一个广义择一性定理.在目标为锥凸和满足 推广了的Slater约束规格的条件下,我们利用本文的择一性定理,给出了集一集映射 向量极值问题关于锥-超极小解的Lagrange乘子定理和鞍点定理. 相似文献