Research On Numerical Algorithm For Linear Complementarity Problem

The complementarity problem is one of the most important research subjects in mathematical programming.It has a wide range of applications in engineering and economics.After decades of research,the subject has developed into a very fruitful discipline.The developments include a rich mathematical theory and a host of effective solution algorithms.Since some elements may involve uncertain data in many practical problems,the stochastic versions of complementarity problems has drawn much attention in the recent literature.The stochastic linear complementarity problem is the basic problem of stochastic complementarity problem.The study of theories and algorithms of stochastic linear complementarity problems has important reference value to stochastic complementarity problems.So we focus on the basic linear complementarity problems and the stochastic linear complementarity problems.The structure and main contents of this thesis are summarized as follows:In the first chapter,we consider the basic linear complementarity problems and the Levenberg-Marquardt-type methods is given.And in the general conditions,the global convergence result is also proved.The numerical experiments are presented to show the effectiveness of this method.In the second chapter,we consider a class of stochastic linear complementarity problems with finitely many elements.We propose a feasible nonsmooth Levenberg-Marquardt-type method.And the corresponding global convergence result and the numerical experiments are also given.In the third chapter,we consider the stochastic generalized linear complementarity problems and propose a new conjugate gradient projection method.In the general conditions,we give the global convergence result and the related numerical experiments of the given method.