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101.
Nonlinear complementarity as unconstrained optimization 总被引:8,自引:0,他引:8
C. Kanzow 《Journal of Optimization Theory and Applications》1996,88(1):139-155
Several methods for solving the nonlinear complementarity problem (NCP) are developed. These methods are generalizations of the recently proposed algorithms of Mangasarian and Solodov (Ref. 1) and are based on an unconstrianed minimization formulation of the nonlinear complementarity problem. It is shown that, under certain assumptions, any stationary point of the unconstrained objective function is already a solution of NCP. In particulr, these assumptions are satisfied by the mangasarian and Soolodov implicit Lagranian functioin. Furthermore, a special Newton-type method is suggested, and conditions for its local quadratic convergence are given. Finally, some preliminary numerical results are presented.The author would like to thank Dr. Oswald Knoth (Leipzig) for pointing out that the equivalence of Lemma 2.2. is not true for complementarity problems which have no solutions. He is also grateful to the anonymous referencees for their helpful comments. 相似文献
102.
Chenliang Li Jinping Zeng 《高等学校计算数学学报(英文版)》2006,15(4):289-298
In this paper we consider some synchronous and asynchronous multisplitting and Schwarz methods for solving the linear complementarity problems. We establish some convergence theorems of the methods by using the concept of M-splitting. 相似文献
103.
For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported. 相似文献
104.
Marek J. Śmietański 《Numerical Algorithms》2006,41(3):219-238
A new version of finite difference approximation of the generalized Jacobian for a finite max function is constructed. Numerical
results are reported for the generalized Newton methods using this approximation. 相似文献
105.
The notion of infinitesimal exceptional family of elements for an ordered pair of mappings is introduced. By using a special inversion mapping, a duality between the exceptional family of elements for an ordered pair of mappings and the infinitesimal exceptional family of elements for an ordered pair of mappings is presented. By using this duality and the notion of scalar derivatives, existence theorems for implicit complementarity problems in Hilbert spaces are presented.Communicated by F. A. PotraThe second author was supported by the Hungarian Research Grants OTKA T043276 and T043241. 相似文献
106.
A. Shapiro 《Journal of Optimization Theory and Applications》2006,128(1):221-243
In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation
of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions.
We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems 相似文献
107.
VariationalInequalityandComplementarityProblemforSet-ValuedMappingwithApplication¥ZhangCongjun(DepartmentofMathematics,Huaibe... 相似文献
108.
Chang-fengMa Pu-yanNie Guo-pingLiang 《计算数学(英文版)》2003,21(6):747-758
The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm. 相似文献
109.
LIDONGHUI 《高校应用数学学报(英文版)》1996,11(4):487-496
In this paper, we propose an inexact clamped Newton method for solving nonlinear complementarity problems based on the equivalent B-differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given. 相似文献
110.
Jundi Ding Hongyou Yin 《高等学校计算数学学报(英文版)》2007,16(2):155-163
In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method. 相似文献