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随机交通均衡配流模型及其等价的变分不等式问题 总被引:7,自引:0,他引:7
本文讨论了交通网络系统的随机用户均衡原理的数学表述问题.在路段出行成本是流量的单调函数的较弱条件下,对具有固定需求和弹性需求的模式,首次证明了随机均衡配流模型可表示为一个变分不等式问题,同时也说明了该变分不等式问题与相应的互补问题以及一个凸规划问题之间的等价关系. 相似文献
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1.引言 变分不等式问题在数学规划中起着重要作用,它最初作为研究偏微分方程的工具,首先由 Fishera和 Stampacchia等于六十年代初提出,可参看[1]及其参考文献,之后也被广泛用于研究经济学和运筹学等领域中的均衡模型,互补问题和凸规划问题都是变分不等式问题的特殊情形,文献[2]对有限维变分不等式问题和非线性互补问题的理论、算法及应用作了十分全面的综述.设 C是实有限维空间 Rn,的非空闲凸子集, F是 Rn → Rn的映射,本文讨论的变分不等式问题VI(C,F)是: 求向量r*∈C.使得:F(… 相似文献
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本文研究了一类带等式和不等式约束的双层规划问题,首先利用下层问题的KKT条件将双层规划转化为单层约束规划问题;其次结合罚函数法,构造了一种新的填充函数,并探讨了它的性质;最后基于构造的填充函数,获得了一种求解双层规划问题的填充函数法,并通过数值实验说明了该算法的可行性. 相似文献
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结合罚函数思想和广义梯度投影技术,提出求解非线性互补约束数学规划问题的一个广义梯度投影罚算法.首先,通过扰动技术和广义互补函数,将原问题转化为序列带参数的近似的标准非线性规划;其次,利用广义梯度投影矩阵构造搜索方向的显式表达式.一个特殊的罚函数作为效益函数,而且搜索方向能保证效益函数的下降性.在适当的假设条件下算法具有全局收敛性. 相似文献
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1 引言 互补问题在最优化中有着广泛的应用,例如线性规划中的对偶问题,非线性规划中求稳定点的KKT条件以及变分不等式的求解都可以转化为互补问题,另外,某些均衡网络设计问题、信号最优化问题以及交通配置等问题也可利用互补问题来求解. 相似文献
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本文将单位映射变分不等式和互补问题的解的存在性定理推广到集值映射上.讨论了集值映射互补问题的解与Kakutani不动点之间关系,以及集值映射互补问题的解的计算方法.最后给出了它们在不可微规划中的应用. 相似文献
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相补问题及其对数学规划的应用 总被引:4,自引:0,他引:4
一、引言 变分不等式理论内容十分丰富,它不仅具有深刻的数学思想,而且为许多具有重要理论和应用价值的问题的研究提供良好的框架(见[1,10,24])。 与变分不等式理论紧密相联系的是相补问题。这一问题的研究最早开始于60年代Lemke,Cottle和Damtzig的工作。以后随着变分不等式理论的发展,相补问题的理论也得到深入地发展(见[1,3—6,13,22,23])。现在相补问题的理论不仅应用于控制 相似文献
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Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints 总被引:7,自引:0,他引:7
Terry L. Friesz Roger L. Tobin Hsun-Jung Cho Nihal J. Mehta 《Mathematical Programming》1990,48(1-3):265-284
In this paper we consider heuristic algorithms for a special case of the generalized bilevel mathematical programming problem in which one of the levels is represented as a variational inequality problem. Such problems arise in network design and economic planning. We obtain derivative information needed to implement these algorithms for such bilevel problems from the theory of sensitivity analysis for variational inequalities. We provide computational results for several numerical examples. 相似文献
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B. S. Mordukhovich 《Mathematical Programming》2009,120(1):261-283
The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept
is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant
from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations
via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various
classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization
theory and its applications. Based on robust generalized differential calculus, we derive new results giving pointwise necessary
and sufficient conditions for linear suboptimality in general MPECs and its important specifications involving variational
and quasivariational inequalities, implicit complementarity problems, etc.
Research was partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research
Council under grant DP-0451168. 相似文献
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G. Isac 《Journal of Global Optimization》2005,31(3):405-420
In several recent papers we obtained existence theorems for complementarity problems and variational inequalities using for each of them a particular notion of exceptional family of elements. Now, in this paper we introduce a new notion of exceptional family of elements. This notion is based on an Implicit Leray-Schauder Alternative. By this new notion we obtain a unification of the study of solvability of complementarity problems and of variational inequalities. The paper is finished with a section dedicated to variational inequalities with δ-pseudomonotone operators. 相似文献
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该文提出并分析了用广义投影方法解Noor型广义变分不等式问题.在较弱的条件下考虑了一个迭代格式的收敛性.由于广义变分不等式包含了许多变分不等式和相补问题为特例,因此该文得出的结果可以应用到这些问题中.这些结果是以前众多学者所做工作的完善和改进. 相似文献
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Solution differentiability for variational inequalities 总被引:1,自引:0,他引:1
Jerzy Kyparisis 《Mathematical Programming》1990,48(1-3):285-301
In this paper we study solution differentiability properties for variational inequalities. We characterize Fréchet differentiability of perturbed solutions to parametric variational inequality problems defined on polyhedral sets. Our result extends the recent result of Pang and it directly specializes to nonlinear complementarity problems, variational inequality problems defined on perturbed sets and to nonlinear programming problems. 相似文献
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Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2006,324(2):1417-1428
In this paper, we introduce and analyze a new class of equilibrium problems known as general hemiequilibrium problems. It is shown that this class includes hemiequilibrium problems, hemivariational inequalities and complementarity problems as special cases. We use the auxiliary principle techniques to suggest some iterative-type methods for solving multivalued hemiequilibrium problems. We also analyze the convergence analysis of these new iterative methods under some mild conditions. As special cases, we obtain several new and known methods for solving variational inequalities and equilibrium problems. 相似文献
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Merit functions for general variational inequalities 总被引:1,自引:0,他引:1
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2006,316(2):736-752
In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities. 相似文献
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This paper studies the variational inequality problem over a fuzzy domain and variational inequalities for fuzzy mappings over a fuzzy domain. It is shown that such problems can be reduced to bilevel programming problems. A penalty function algorithm is introduced with a convergence proof. Numerical examples are also included to illustrate the solution procedure. 相似文献
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Exact Penalty Functions for Convex Bilevel Programming Problems 总被引:2,自引:0,他引:2
Liu G. S. Han J. Y. Zhang J. Z. 《Journal of Optimization Theory and Applications》2001,110(3):621-643
In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given. 相似文献
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MUHAMMAD ASLAM NOOR 《Journal of Global Optimization》2000,18(1):75-89
In this paper, we suggest and analyze a number of resolvent-splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution. The convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator. Proof of convergence is very simple. Our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems. The new results are versatile and are easy to implement. 相似文献