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1.
Sensitivity Analysis for Quasi-Variational Inequalities 总被引:12,自引:0,他引:12
M. A. Noor 《Journal of Optimization Theory and Applications》1997,95(2):399-407
In this paper, we develop a sensitivity analysis framework for quasi-variational inequalities using the Wiener–Hopf equations technique without assuming the differentiability of the given data. 相似文献
2.
In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study
generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized
vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized
vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP))
is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone
maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These
existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results
of this paper extend recent results in the literature. They are obtained in a more general setting. 相似文献
3.
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
4.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):457-475
In this paper, we deal with the following problem: given a real normed space E with topological dual E*, a closed convex set XE, two multifunctions :X2X and
, find
such that
We extend to the above problem a result established by Ricceri for the case (x)X, where in particular the multifunction is required only to satisfy the following very general assumption: each set (x) is nonempty, convex, and weakly-star compact, and for each yX–:X the set
is compactly closed. Our result also gives a partial affirmative answer to a conjecture raised by Ricceri himself. 相似文献
5.
6.
Monica Patriche 《Numerical Functional Analysis & Optimization》2014,35(7-9):1152-1173
We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies. 相似文献
7.
借助集值优化问题的灵敏度分析,讨论了下层无扰动,上层带扰动参数的二层多目标最优化问题的灵敏度分析. 相似文献
8.
本文在序锥P具有弱紧基的条件下讨论了集值映射F的切导数与F P的切导数之间的关系;引进了集值映射的新的上半局部Lipschitz概念,利用这个概念,我们在有限维空间中给出了多目标最优化问题的灵敏度分析的一个新的结果. 相似文献
9.
10.
The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints. 相似文献
11.
T. Q. Bao P. Gupta B. S. Mordukhovich 《Journal of Optimization Theory and Applications》2007,135(2):179-203
We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations
in the form
where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variational inequalities
and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the
general problems under consideration and for their important specifications by using modern tools of variational analysis
and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical
example from bilevel programming with convex while nondifferentiable data. 相似文献
12.
A. Balbás E. Galperin P. Jiménez. Guerra 《Journal of Optimization Theory and Applications》2005,126(2):247-264
The paper presents a sensitivity analysis of Pareto solutions on the basis of the Karush-Kuhn-Tucker (KKT) necessary conditions applied to nonlinear multiobjective programs (MOP) continuously depending on a parameter. Since the KKT conditions are of the first order, the sensitivity properties are considered in the first approximation. An analogue of the shadow prices, well known for scalar linear programs, is obtained for nonlinear MOPs. Two types of sensitivity are investigated: sensitivity in the state space (on the Pareto set) and sensitivity in the cost function space (on the balance set) for a vector cost function. The results obtained can be used in applications for sensitivity computation under small variations of parameters. Illustrative examples are presented.Research of this author was partially supported by Grant BEC2003-09067-C04-03.Research of this author was partially supported by NSERC Grant RGPIN-3492-00.Research of this author was partially supported by Grant BEC2003-09067-C04-02. 相似文献
13.
黄时祥 《数学的实践与认识》2007,37(5):83-88
利用极大熵方法将带多个非线性不等式约束和多个非线性等式约束的多目标规划问题变为两个非线性不等式约束的单个可微的目标函数优化问题,并结合区间分析知识给出一种新的解决多目标规划问题的区间方法. 相似文献
14.
E. A. Galperin 《Journal of Optimization Theory and Applications》1997,93(3):533-545
There is much controversy about the balance space approach, introduced first in Ref. 1, pp. 138–140, with the consideration of the balance number and balance vectors, and then further developed in Ref. 2, with the consideration of balance points and balance sets. There were attempts to identify the balance space approach with some other methods of multiobjective optimization, notably the method proposed in Ref. 3 and most recently Pareto analysis, as presented in Ref. 4. In this paper, we compare Pareto analysis with the balance space approach on several examples to demonstrate the interrelation and the differences of the two methods. As a byproduct, it is shown that, in some cases, the entire Pareto sets, proper and adjoint, can be determined very simply, without any special investigation of the (nonscalarized, nonconvex) multiobjective global optimization problem. The method of parameter introduction is presented in application to determining the Pareto sets and balance set. The use of computer graphics software complemented with the Gauss–Jordan matrix reduction algorithm is proposed for a class of otherwise intractable problems with nonconvex constraint sets. 相似文献
15.
In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order necessary and sufficient conditions for efficiency. 相似文献
16.
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
17.
G. P. Crespi A. Guerraggio M. Rocca 《Journal of Optimization Theory and Applications》2007,132(1):213-226
In this paper, we give notions of well posedness for a vector optimization problem and a vector variational inequality of
the differential type. First, the basic properties of well-posed vector optimization problems are studied and the case of
C-quasiconvex problems is explored. Further, we investigate the links between the well posedness of a vector optimization problem
and of a vector variational inequality. We show that, under the convexity of the objective function f, the two notions coincide. These results extend properties which are well known in scalar optimization.
Communicated by F. Giannessi 相似文献
18.
On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case 总被引:2,自引:0,他引:2
Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn–Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated. 相似文献
19.
20.
Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated. 相似文献