Research On Smooth Gradient Algorithms For Tensor Complementarity Problem

The tensor complementarity problem,as a special class of nonlinear complementarity problems,has attracted a lot of attention from the domestic and foreign scholars in the field of optimization in recent years.With the widely applications of tensor in signal processing,data analysis,image processing and other fields,the tensor complementarity problem also has been extensively studied from theory to solution methods and applications.In this thesis,the smoothing conjugate gradient methods for solving the tensor complementarity problem are studied.The main research contents of this thesis are as follows:(1)The development of complementarity problems and the tensor complementarity problem is briefly described.Through the transformation of the tensor complementarity problem by complementary functions and smoothing functions,the equivalence relation between the tensor complementarity problem and unconstrained optimization problem is constructed.(2)A new smoothing spectral conjugate gradient method for solving the tensor complementarity problem under Armijo line search and a new smoothing Hestenes-Stiefel(HS)conjugate gradient method for solving the tensor complementarity problem under Wolfe type line search are proposed respectively.The global convergence analysis and related numerical experiments of each method are given under mild conditions.(3)The application of tensor complementarity problem to solve a class of multiperson noncooperative game problems is studied.Using the equivalence between this kind of game problem and tensor complementarity problem,the multi-person noncooperative game problem is solved by the proposed smoothing gradient method.The relevant numerical experiments are given to show the stability and effectiveness of the method.