• 论文 •

一种求解非线性互补问题的方法及其收敛性

1. 北京交通大学应用数学系,曲阜师范大学运筹学研究所,华东师范大学数学系 北京 100044；曲阜师范大学运筹学研究所,山东 276826,山东 276826,上海 200062；解放军镇江船艇学院船艇指挥系,镇江 212003
• 出版日期:2006-03-14 发布日期:2006-03-14

A METHOD FOR SOLVING NONLINEAR COMPLEMENTARITY PROBLEMS AND ITS CONVERGENCE PROPERTIES

1. Qu Biao (Department of Applied Mathematics,Beijing Jiaotong University,Beijing 100044,China;Institute of Operations Research,Qufu Normal University,Shandong 276826,China) Wang Changyu (Institute of Operations Research,Qufu Normal University,Shandong 276826,China) Zhang Shuxia (Department of Mathematics,East China Normal University,Shanghai,200062,China;Department of Watercraft Command,Zhenjiang Watercraft College,Zhenjiang,212003,China)
• Online:2006-03-14 Published:2006-03-14

In this paper,we establish a method for the solution of nonlinear comple- mentarity problem.This method is a combination of Newton method and the extragradient method.It is shown that this method is globally and superlineraly convergent.Furthermore,under appropriate conditions,we give a finite termi- nation result.Preliminary numerical results show that the proposed method is promising.
()
 [1]M.V.Solodov and B.F.Svaiter,A truly globally convergent Newton-type method for the monotone nonlinear complementarity problem,SIAM J.OPTIM,10:2(2000),605-625. [2]N.H.Xiu and J.Z.Zhang,Some recent advances in projection-type methods for variational inequalities,Journal of Computational and Applied Mathematics,152(2003),559-585. [3]D.Sun,A class of iterative methods for solving nonlinear projection equations,Journal of Optimization Theory and Applications,91:1(1996),123-140. [4]P.H.Calamai and J.J.Moré,Projected gradient methods for linearly constrained problems,Math.Programming,39(1987),93-116. [5]J.Z.Zhang and N.H.Xiu,New projection-type methods for monotone LCP with finite termination,Numer.Math.,92(2002),179-195. [6]C.Geiger and C.Kanzow,On the resolution of monotone complementarity problems,Comput.Optim.Appl.,5(1996),155-173. [7]C.Kanzow,Some equation-based methods for the nonlinear complementarity problems,Optim.Methods Software,3(1994),327-340. [8]H.Y.Jiang and L.Q.Qi,A new nonsmooth equations approach to nonlinear complementarity problems,SIAM J.Control Optim.,45(1997),178-193. [9]P.Marcotte,D.L.Zhu,Weak Sharp Solutions of Variational Inequalities,SIAM Journal on Optimization,9:1(1998),179-189. [10]M.V.Solodov,P.Tseng,Some Methods Based on the D-gap Function for Solving Monotone Variational Inequalities,Comput.Optim.Appl.,17(2000),255-277. [11]F.Facchinei,J.S.Pang,Finite-demensional variational inequalities and complementarity problems,Spring-Verlag New York,Inc.,2003. [12]韩继业，修乃华，戚厚铎，《非线性互补理论与算法》，上海科学技术出版社，2006． [13]J.S.Pang and S.A.Gabriel,NE/SQP:A robust algorithm for the nonlinear complementarity problem,Math.Programming,60(1993),295-337. [14]O.L.Mangasarian and M.V.Solodov,Nonlinear complementarity as unconstrained and constrained minimization,Math.Programming(Series B),62(1993),277-297. [15]L.Mathiesen,An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model:An example,Math.Programming,37(1987),1-18.
 No related articles found!