共查询到20条相似文献,搜索用时 15 毫秒
1.
Luis Rodríguez-Marín Miguel Sama 《Journal of Optimization Theory and Applications》2013,156(3):683-700
This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal. 相似文献
2.
Xi Yin Zheng 《Set-Valued and Variational Analysis》2009,17(4):389-408
In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping
whose graph is the union of finitely many polyhedra. We establish some results on structure and connectedness of the weak
Pareto solution set, Pareto solution set, weak Pareto optimal value set and Pareto optimal value set of (SVOP). In particular,
we improve and generalize Arrow, Barankin and Blackwell’s classical results on linear vector optimization problems in Euclidean
spaces. 相似文献
3.
S. K. Mishra B. B. Upadhyay Le Thi Hoai An 《Journal of Optimization Theory and Applications》2014,160(3):763-777
This paper deals with the minimization of a class of nonsmooth pseudolinear functions over a closed and convex set subject to linear inequality constraints. We establish several Lagrange multiplier characterizations of the solution set of the minimization problem by using the properties of locally Lipschitz pseudolinear functions. We also consider a constrained nonsmooth vector pseudolinear optimization problem and derive certain conditions, under which an efficient solution becomes a properly efficient solution. The results presented in this paper are more general than those existing in the literature. 相似文献
4.
A. J. Zaslavski 《Journal of Optimization Theory and Applications》2014,162(2):649-664
In this paper, we use the penalty approach in order to study a class of constrained vector minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property iff there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems, we establish the generalized exact penalty property and obtain an estimation of the exact penalty. 相似文献
5.
We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new properties, pseudonormality and quasinormality, emerge as central within the taxonomy of interesting constraint characteristics. In the case where there is no abstract set constraint, these properties provide the connecting link between the classical constraint qualifications and two distinct pathways to the existence of Lagrange multipliers: one involving the notion of quasiregularity and the Farkas lemma, and the other involving the use of exact penalty functions. The second pathway also applies in the general case where there is an abstract set constraint. 相似文献
6.
In this paper, we propose two kinds of optimality concepts, called the sharp minima and the weak sharp minima, for a constrained set-valued optimization problem. Subsequently, we extend the Fermat rules for the local minima of the constrained set-valued optimization problem to the sharp minima and the weak sharp minima in Banach spaces or Asplund spaces, by means of the Mordukhovich generalized differentiation and the normal cone. As applications, we investigate the generalized inequality systems with constraints, and get some characterizations of error bounds for the constrained generalized inequality systems in convex and nonconvex cases. 相似文献
7.
Duan Yarui Jiao Liguo Wu Pengcheng Zhou Yuying 《Journal of Optimization Theory and Applications》2022,195(1):148-171
Journal of Optimization Theory and Applications - This paper deals with a vector polynomial optimization problem over a basic closed semi-algebraic set. By invoking some powerful tools from real... 相似文献
8.
César Gutiérrez Bienvenido Jiménez Vicente Novo 《Computational Optimization and Applications》2006,35(3):305-324
This work deals with approximate solutions in vector optimization problems. These solutions frequently appear when an iterative
algorithm is used to solve a vector optimization problem. We consider a concept of approximate efficiency introduced by Kutateladze
and widely used in the literature to study this kind of solutions. Necessary and sufficient conditions for Kutateladze’s approximate
solutions are given through scalarization, in such a way that these points are approximate solutions for a scalar optimization
problem. Necessary conditions are obtained by using gauge functionals while monotone functionals are considered to attain
sufficient conditions. Two properties are then introduced to describe the idea of parametric representation of the approximate
efficient set. Finally, through scalarization, characterizations and parametric representations for the set of approximate
solutions in convex and nonconvex vector optimization problems are proved and the obtained results are applied to Pareto problems.
AMS Classification:90C29, 49M37
This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194. 相似文献
9.
Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems 总被引:1,自引:0,他引:1
In this paper, we introduce a new concept of ϵ-efficiency for vector optimization problems. This extends and unifies various notions of approximate solutions in the literature.
Some properties for this new class of approximate solutions are established, and several existence results, as well as nonlinear
scalarizations, are obtained by means of the Ekeland’s variational principle. Moreover, under the assumption of generalized
subconvex functions, we derive the linear scalarization and the Lagrange multiplier rule for approximate solutions based on
the scalarization in Asplund spaces. 相似文献
10.
11.
Behnam Soleimani 《Journal of Optimization Theory and Applications》2014,162(2):605-632
In this paper, we deal with approximate solutions in vector-optimization problems with respect to a variable order structure. In the case of exact solutions of a vector optimization problem, especially in the variable order case, authors use a cone or a pointed convex cone-valued map in order to describe the solution concepts but in this paper, we use a set-valued map and this map is not a (pointed convex) cone-valued map necessarily. We characterize these solution concepts by a general scalarization method by means of nonlinear functionals. In the last section, an extension of Ekeland’s variational principle for a vector optimization problem with a variable order structure is given. 相似文献
12.
In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and
nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining
the same precision in the vector problem as in the scalarization.
This research was partially supported by the Ministerio de Educación y Ciencia (Spain), Project MTM2006-02629 and by the Consejería
de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees
for helpful comments and suggestions. 相似文献
13.
Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization 总被引:10,自引:0,他引:10
In the first part of this paper, the Demyanov difference of two sets is considered. An expression for the Demyanov difference of two sets, which are the convex hulls of a finite number of points, is presented. In the second part, first-order necessary optimality conditions of the Lagrange multiplier type, for quasidifferentiable optimization with equality and inequality constraints, are given by means of the Demyanov difference of subdifferential and negative superdifferential. 相似文献
14.
Alexander J. Zaslavski 《Set-Valued Analysis》2007,15(3):223-237
In this paper we use the penalty approach in order to study constrained minimization problems in a complete metric space with
locally Lipschitzian mixed constraints. A penalty function is said to have the exact penalty property if there is a penalty
coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem.
In this paper we establish sufficient conditions for the exact penalty property.
相似文献
15.
Approximate nondominated solutions of real vector optimization problems are characterized using the concept of translated
cones. Relationships between these solutions and Pareto nondominated points are examined, and the problem of optimizing over
the set of approximate solutions is addressed.
This research was supported by the National Science Foundation, Grant DMS-0425768, and by the Automotive Research Center,
a US Army TACOM Center of Excellence for Modeling and Simulation of Ground Vehicles at the University of Michigan 相似文献
16.
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
17.
龙宪军 《数学物理学报(A辑)》2014,34(3):593-602
在Asplund空间中,研究了非凸向量均衡问题近似解的最优性条件.借助Mordukhovich次可微概念,在没有任何凸性条件下获得了向量均衡问题εe-拟弱有效解,εe-拟Henig有效解,εe-拟全局有效解以及εe-拟有效解的必要最优性条件.作为它的应用,还给出了非凸向量优化问题近似解的最优性条件. 相似文献
18.
希氏空间中算子样条插值及算子方程的近似解 总被引:2,自引:0,他引:2
本文首先讨论希氏空间中由有界线性算子T确定的抽象插值样条(本文称T样条)的构造,通过引入新的内积得到T样条的投影特征和表达式.然后研究算子方程Tx=y的投影近似解和T样条近似解,并给出了两种近似解误差之间的关系. 相似文献
19.
20.
Using the additive weight method of vector optimization problems and the method of essential solutions, we study some continuity
properties of the mapping which associates the set of efficient solutions S(f) to the objective function f. To understand such properties, the key point is to consider the stability of additive weight solutions and the relationship
between efficient solutions and additive weight solutions. 相似文献