共查询到20条相似文献,搜索用时 10 毫秒
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We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.This research was supported by a Central Research Grant of The Hong Kong Polytechnic University (Grant No. G-T 507). Research of the first author was also supported by the National Natural Science Foundation of PR China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M). 相似文献
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In this paper, the Pareto solution set of a piecewise linear multiobjective optimization problem in a normed space is shown
to be the union of finitely many semiclosed polyhedra. If the problem is further assumed to be cone-convex, then it has the
global weak sharp minimum property. 相似文献
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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 properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints. 相似文献
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本文研究了一类带不等式约束的多目标优化问题,给出了该类问题的有效解的一些充分必要条件,在适当条件下利用线性标量化方法证明了其有效解和真有效解的等价性。本文的主要结论是对最近一些文献中相应结果的改进与推广。 相似文献
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In this paper, we are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. We introduce a second-order constraint qualification, which is a generalization of the Abadie constraint qualification and derive second-order Kuhn-Tucker type necessary conditions for efficiency under the constraint qualification. Moreover, we give some conditions which ensure the constraint qualification holds. 相似文献
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Sanaz Sadeghi S. Morteza Mirdehghan 《Journal of Optimization Theory and Applications》2018,178(2):591-613
Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions. 相似文献
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多目标规划ak-较多有效解类的有效性充分条件 总被引:1,自引:0,他引:1
丁鸿生 《应用数学与计算数学学报》2000,(1)
在文[3]引进多目标规划问题的带双参数a和k的ak-较多有效解, 并且给出了此类解的有效性必要条件。本文在一定凸性的假设下证明了ak-较多 有效解和ak-弱较多有效解的几个有效性充分条件. 相似文献
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On Approximate Efficiency in Multiobjective Programming 总被引:2,自引:0,他引:2
This paper is focused on approximate (
-efficient) solutions of multiobjective mathematical programs. We introduce a new
-efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these
-efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different
-efficiency sets. Several classical
-efficiency notions are considered in order to show the concepts introduced and the results obtained.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194. 相似文献
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多目标优化问题Proximal真有效解的最优性条件 总被引:1,自引:1,他引:0
在广义凸性假设下,给出了集合proximal真有效点的线性标量化,并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上,得到proximal真有效解的最优性条件.最后,利用proximal次微分,得到了proximal真有效解的模糊型最优性条件. 相似文献
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We derive a simple sufficient condition for a point a∈S?X be a local minimum of f: X → R on S. This condition is of the first order in its nature and takes into account the derivative (or some generalization of it) in a neighborhood of a. Applications like a sufficient condition for (a, b)∈ S × T ? X × Y be a saddle-point of a bivariate function f: X × Y ? R are also proposed. 相似文献
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In this note, we prove that the convergence results for vector optimization problems with equilibrium constraints presented
in Wu and Cheng (J. Optim. Theory Appl. 125, 453–472, 2005) are not correct. Actually, we show that results of this type cannot be established at all. This is due to the possible lack,
even under nice assumptions, of lower convergence of the solution map for equilibrium problems, already deeply investigated
in Loridan and Morgan (Optimization 20, 819–836, 1989) and Lignola and Morgan (J. Optim. Theory Appl. 93, 575–596, 1997). 相似文献
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We give a suitable example to show a gap between multiobjective optimization and single-objective optimization, which solves a problem proposed in Refs. 1–2. 相似文献
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Let r and s be nonnegative integers, and let G be a graph of order at least 3r + 4s. In Bialostocki et al. (Discrete Math 308:5886–5890, 2008), conjectured that if the minimum degree of G is at least 2r + 3s, then G contains a collection of r + s vertex-disjoint cycles such that s of them are chorded cycles, and they showed that the conjecture is true for r = 0, s = 2 and for s = 1. In this paper, we settle this conjecture completely by proving the following stronger statement; if the minimum degree
sum of two nonadjacent vertices is at least 4r + 6s−1, then G contains a collection of r + s vertex-disjoint cycles such that s of them are chorded cycles. 相似文献
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Monica Bianchi Enrico Miglierina Elena Molho Rita Pini 《Set-Valued and Variational Analysis》2013,21(1):47-65
Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem defined via m convex C 1,1 objective functions on a given closed ball in ? n . Two approaches are proposed: the first one adopts a local point of view around a given solution point, whereas the second one considers the solution set as a whole. A comparison between the two notions of well-conditioned problem is developed. We underline that both the condition numbers introduced in the present work reduce to the same condition number proposed by Zolezzi in 2003, in the special case of the scalar optimization problem considered there. A pseudodistance between functions is defined such that the condition number provides an upper bound on how far from a well–conditioned function f a perturbed function g can be chosen in order that g is well–conditioned too. For both the local and the global approach an extension of classical Eckart–Young distance theorem is proved, even if only a special class of perturbations is considered. 相似文献
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Regina S. Burachik Juan Enrique Martínez-Legaz Marco Rocco 《Set-Valued and Variational Analysis》2010,18(3-4):327-335
We establish minimal conditions under which two maximal monotone operators coincide. Our first result is inspired by an analogous result for subdifferentials of convex functions. In particular, we prove that two maximal monotone operators T,S which share the same convex-like domain D coincide whenever $T(x)\cap S(x)\not=\emptyset $ for every x?∈?D. We extend our result to the setting of enlargements of maximal monotone operators. More precisely, we prove that two operators coincide as long as the enlargements have nonempty intersection at each point of their common domain, assumed to be open. We then use this to obtain new facts for convex functions: we show that the difference of two proper lower semicontinuous and convex functions whose subdifferentials have a common open domain is constant if and only if their ε-subdifferentials intersect at every point of that domain. 相似文献