Projection Algorithm For Random Tensor Complementarity Problem

Tensor complementarity problem is an important research topic in the field of optimization,which has a wide range of applications in game theory,hypergraph clustering and related fields.Besides,considering that many uncertain factors are often involved in practical problems,researchers began to study the stochastic tensor complementarity problem with stochastic variables.In this thesis,we mainly study the projected method for solving stochastic tensor complementarity problem.The specific contents of this thesis are as follows:(1)We introduce the basic definition and calculation of tensors,as well as the basic forms of tensor complementarity problem and stochastic tensor complementarity problem,and briefly describe the development of related theories and methods.(2)We study the discrete stochastic tensor complementarity problem.The projected Levenberg-Marquardt method and a new semismooth projected Newton method combining the Barzilai-Borwein step size and non-monotonic line search technique are used to solve this problem.Under certain conditions,the global convergence of proposed methods is obtained.Related numerical experiments show that these two methods are effective to solve the discrete stochastic tensor complementarity problem.(3)We study the stochastic tensor complementarity problem.Based on the expected residual minimization model,the problem is transformed into an optimization problem with non-negative constraints,and the new semismooth projected Newton method is used to solve this problem.Related numerical experiments show that this method can effectively solve the stochastic tensor complementarity problem.