| Stochastic trust region methods are an important class of numerical computational methods for solving stochastic nonlinear optimization.With the development and application of electronic computers,the theory and methods of nonlinear optimization have evolved considerably.In this thesis,an algorithms for a class of stochastic equationally constrained optimization problems are investigated.It mainly contains the following contents.Introduces the research background of stochastic optimization algorithms and the current state of research at home and abroad,and gives a model of the stochastic constrained optimization problem under study.Two effective solution methods are proposed for stochastic optimization problems.First,the objective and constraint functions of the stochastic equation constraint problem are used to construct the Lipschitz continuous penalty function,and this construction makes the complexity of the computation much lower.In each iteration,the stochastic gradient of the penalty function and the Hessian approximation are derived to model the stochastic trust region and solve the stochastic trust region subproblem to obtain the trial step.The convergence of the stochastic trust region method is demonstrated under certain conditions.Numerical results show that the algorithm is efficient and can solve non-convex stochastic optimization problems.Secondly,a stochastic trust region method based on the Fletcher penalty function is proposed for the stochastic equation constrained optimization problem.In each iteration,the CDT subproblem is created and solved to obtain a trial step.The Fletcher penalty function is constructed to determine whether the trial step is valid in the framework of the trust region.The algorithm is shown to converge under certain conditions.Numerical results show that the algorithm is effective for solving stochastic equation constrained problems. |
