Research On The Expected Residual Minimization Method For The Random Tensor Complementarity Proble

With the rapid development of tensor optimization problem in the field of optimization,stochastic tensor complementarity problem has been widely studied from theory to solution methods.In this thesis,the expected residual minimization method for solving stochastic tensor complementarity problem is studied.The main research contents are as follows:(1)The development status of complementarity problem,stochastic complementarity problem and stochastic tensor complementarity problem is briefly described.The expected value method,the expected residual minimization method,the stochastic programming method with equilibrium constraints and the unconstrained optimization reformulation method for solving stochastic complementarity problem are introduced.Furthermore,the expected value method and the expected residual minimization method for solving stochastic tensor complementarity problem are given.(2)The expected residual minimization method for solving stochastic tensor complementarity problem is studied.The equivalence relationship between stochastic tensor complementarity problem and nonnegative constrained optimization problem is constructed by the transformation of the restricted nonlinear complementarity function and its smooth function for stochastic tensor complementarity problem.A smoothing projected Hestenes-Stiefel(HS)method for solving stochastic tensor complementarity problem is proposed.The global convergence analysis and relevant numerical experiments are given.The numerical results show the stability and efficiency of the method.(3)The expected residual minimization problem for stochastic tensor complementarity problem transformed by Fischer-Burmeister(FB)function,penalty FB function and the min function is considered.The properties of corresponding expected residual functions are studied.The smoothing projected HS method and the smoothing projected Polak-RibierePolyak(PRP)method based on these three nonlinear complementarity functions are proposed,respectively.The relevant convergence analysis and numerical examples of methods are also given.