Algorithm Research On A Class Of Generalized Stochastic Linear Complementarity Problems

Complementarity problems,as one of the important topics in mathematical programming research,plays an important role in mechanics,science and technology,control and finance.Besides,in solving practical problems,there are many stochastic factors need to be considered,such as traffic,supply and demand.More and more attention has been paid to the complementarity problems with stochastic variables.Therefore,in this paper,based on stochastic linear complementarity problems and absolute value equation problems,a kind of generalized stochastic linear complementarity problems is proposed.We also study the methods for solving this kind of problems.The structure and main research contents of this paper are as follows:In Chapter 1,we introduce the basic situation,researched significance and applications of the linear complementarity problems,absolute value equation problems and stochastic linear complementarity problems.The proposed generalized stochastic linear complementarity problems is also introduced.In Chapter 2,we study the proposed generalized stochastic linear complementarity problems,and give a projected Levenberg-Marquardt method for solving it.The local and global convergence analyses of this method are given.Comparing the numerical results of projected Levenberg-Marquardt method and projected FR conjugate gradient method,we know that the projected Levenberg-Marquardt method is effective.In Chapter 3,we study the proposed generalized stochastic linear complementarity problems,and give a projected trust region method for solving it.The local and global convergence analyses of this method under general condition are given.We apply the generalized stochastic linear complementarity problems to solve the American option pricing problem with stochastic volatility.Related numerical experiments show that the projected trust region method is effective.In Chapter 4,we give the conclusions and prospects of this paper.