共查询到20条相似文献,搜索用时 15 毫秒
1.
《Optimization》2012,61(5):597-627
Our main concern in this article are concepts of nondominatedness w.r.t. a variable ordering structure introduced by Yu [P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), pp. 319–377]. Our studies are motivated by some recent applications e.g. in medical image registration. Restricting ourselves to the case when the values of a cone-valued map defining the ordering structure are Bishop–Phelps cones, we obtain for the first time scalarizing functionals for nondominated elements, Fermat rule, Lagrange multiplier rule and duality results for a single- or set-valued vector optimization problem with a variable ordering structure. 相似文献
2.
In this paper, we first discuss the Painlevé–Kuratowski set convergence of (weak) minimal point set for a convex set, when the set and the ordering cone are both perturbed. Next, we consider a convex vector optimization problem, and take into account perturbations with respect to the feasible set, the objective function and the ordering cone. For this problem, by assuming that the data of the approximate problems converge to the data of the original problem in the sense of Painlevé–Kuratowski convergence and continuous convergence, we establish the Painlevé–Kuratowski set convergence of (weak) minimal point and (weak) efficient point sets of the approximate problems to the corresponding ones of original problem. We also compare our main theorems with existing results related to the same topic. 相似文献
3.
向量优化是数学规划领域中十分重要的研究方向之一,其相关基础理论与基本方法的研究具有非常重要的理论意义与应用价值.近年来,关于近似解的定义及其性质研究已成为向量优化理论与方法研究的热点.现主要介绍国内学者,特别是我们团队在向量优化问题的各类近似解和统一解概念及其发展和各类近似解与统一解的性质研究方面取得的一些重要进展.最后,提出了与向量优化问题的近似解与统一解相关的一些公开问题. 相似文献
4.
Ya. I. Rabinovich 《Computational Mathematics and Mathematical Physics》2006,46(10):1705-1716
The problem of comparison of approximations (approximate solutions to a vector optimization problem) obtained using different numerical methods is considered. In the absence of a priori information about the set of weakly efficient vectors, a scalar function is introduced that enables pair-wise comparison of approximations and establishes a binary preference relation according to which the approximations close (in the sense of the Hausdorff distance) to the set containing all possible efficient vectors are preferable to other approximations. 相似文献
5.
In this paper, we investigate vector complementarity problems with a variable ordering relation. We establish existence results of a solution of a vector complementarity problem under an inclusive type condition. We obtain equivalence results among a vector complementarity problem, a vector variational inequality problem and other related problems. 相似文献
6.
Matthias Ehrgott 《Annals of Operations Research》2006,147(1):343-360
In this paper we consider solution methods for multiobjective integer programming (MOIP) problems based on scalarization.
We define the MOIP, discuss some common scalarizations, and provide a general formulation that encompasses most scalarizations
that have been applied in the MOIP context as special cases. We show that these methods suffer some drawbacks by either only
being able to find supported efficient solutions or introducing constraints that can make the computational effort to solve
the scalarization prohibitive. We show that Lagrangian duality applied to the general scalarization does not remedy the situation.
We also introduce a new scalarization technique, the method of elastic constraints, which is shown to be able to find all
efficient solutions and overcome the computational burden of the scalarizations that use constraints on objective values.
Finally, we present some results from an application in airline crew scheduling as evidence.
This research is partially supported by University of Auckland grant 3602178/9275 and by the Deutsche Forschungsgemeinschaft
grant Ka 477/27-1. 相似文献
7.
In vector optimization with a variable ordering structure, the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications, it was started to develop a comprehensive theory for these vector optimization problems. Thereby, also notions of proper efficiency were generalized to variable ordering structures. In this paper, we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow complete characterizations also in the nonconvex case. 相似文献
8.
利用Gertewitz泛函研究向量优化问题的一类非线性标量化问题. 证明了向量优化问题的(C, \varepsilon)-弱有效解或(C, \varepsilon)-有效解与标量化问题的近似解或严格近似解间的等价关系, 并估计了标量化问题的近似解. 相似文献
9.
Elena-Andreea Florea 《Optimization》2016,65(7):1417-1435
In this paper, we define two new concepts of efficiency for vector optimization with variable ordering structure, namely the sharp and robust efficiencies, and we study their connections with classical concepts of efficiency in vector optimization. Then, we get necessary optimality conditions for them using Fréchet and Mordukhovich calculus coupled with the Gerstewitz’s (Tammer’s) scalarizing functional and openness results for set-valued maps. 相似文献
10.
In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. 相似文献
11.
12.
Peter I. Kogut 《Applicable analysis》2013,92(5):994-1009
We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems. 相似文献
13.
In this paper we introduce several concepts of approximate solutions of set-valued optimization problems with vector and set optimization. We prove existence results and necessary and sufficient conditions by using limit sets. 相似文献
14.
利用G\"{o}pfert等提出的非线性标量化函数给出了向量优化中\varepsilon-真有效解的一个非线性标量化性质, 并提出几个例子对主要结果进行了解释. 相似文献
15.
X. H. Gong 《Journal of Global Optimization》2011,49(4):607-622
In this paper, we give results on Chebyshev scalarization of weakly efficient solution, Henig efficient solution, globally
efficient solution and superefficient solution to the vector equilibrium problems without convexity assumptions. 相似文献
16.
《Optimization》2012,61(12):2091-2116
ABSTRACTThe aim of this paper is, in the setting of normed spaces with a cone K non necessarily solid, to study new relations among set scalarization functions that are extensions of the oriented distance of Hiriart-Urruty. Moreover, we deal with a set scalarization function of sup-inf type, we investigate its relation to the cone-properness and cone-boundedness and it is related to other set scalarizations existing in the literature. In particular, with the norm induced by the Minkowski's functional, we obtain relations with a set scalarization which is an extension of the so called Gerstewitz's scalarization function. 相似文献
17.
Lucelina Batista Santos Marko Rojas-Medar Gabriel Ruiz-Garzn Antonio Rufin-Lizana 《Applied mathematics and computation》2008,200(2):547
In this paper we study the existence of weakly efficient solutions for some nonsmooth and nonconvex vector optimization problems. We consider problems whose objective functions are defined between infinite and finite-dimensional Banach spaces. Our results are stated under hypotheses of generalized convexity and make use of variational-like inequalities. 相似文献
18.
Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invariance properties. We prove that, where the domain contains optimization problems without maximum, there is no non-trivial consistent solution satisfying non-emptiness, translation and multiplication invariance. Moreover, we show that the class of ‘satisficing’ solutions is obtained, if the invariance axioms are replaced with Chernoff’s Choice Axiom. 相似文献
19.
Elisabeth Köbis 《Optimization》2017,66(12):1991-2005
We introduce several variable order relations to compare sets in a linear topological space and we consider set optimization problems equipped with these variable ordering structures. By considering a set approach, we introduce characterizations for optimal solutions and we provide a kind of vectorization result to obtain solutions of set optimization problems equipped with the introduced variable order relations. 相似文献
20.
研究了多目标优化问题的近似解. 首先证明了多面体集是 co-radiant集,并证明了一些性质. 随后研究了多面体集下多目标优化问题近似解的特殊性质. 相似文献