Nonlinear Equality Constrained Optimization Problem Of The Trust Region Filter Algorithm

Feasible Direction method,Penaly function method,Sequential quadratic programming method and reduced Hessian method are applied more extensive for sloving nonlinear constrained optimization problem.Sequential quadratic programming method ia one of the most important method for solving middle scale and small scale nonlinear constrained optimization. In order to make the optimization algorithm has better convergence and numerical results, recently years, optimization strategy are applied in optimization method by Scholars, and good results are achieved. Such as nonmonotonic technology, adaptive technology and filter technology.In this paper,the trust region SQP algorithm for solving the nonlinear equations optimization problems are studied. Algorithm improvements in trust region subproblems and algorithm framework, the basic idea is to improve various optimization strategy into SQP trust region algorithm in order to get good convergence and numerical results.In chapter 1, The basic theory of nonlinear optimization and this paper mainly studies the SQP trust region algorithm are introduced,then several common optimization strategy are introduced. Finally,the trust region SQP filter algorithm are introduced. In chapter 2,the subproblem incompatible and Maratos effects in trust region SQP algorithm for sloving the constrained optimization problem are introduced simply.First,solve trust region subproblems incompatible method and problem solving method are introduced, then the reasons and Maratos effects of commonly used methods of solving Maratos effect is introduced. Finally,the use of test function is introduced.SuKe's research result shows that the improved algorithm framework in the aspects of nonmonotone technique to judge the acceptability can make the testing steps overcame the Maratos effects. In chapter 3, on the base of SuKe'research, the two nonmonotone trust region SQP filter algorithm is given. In the aspect of the trial step,we compute a quasi-normal step and a tangential step for solving the trust region subproblem.Then,the convergence of the improved algorithms under certain condition are analysed.Finally, make two nonmonotone trust region algorithm and SuKe's SQP filter non-monotone SQP trust region algorithm is applied to optimize filter test model, and got good results. The numerical experiments show that the algorithm proposed in this chapter has better numerical effective.The trust region radius of choice will also affect the efficiency of the algorithm is considered. In chapter 1, based on the chapter 3,the proposed algorithm based on trust region subproblem is introduced, and the improvement of the adaptive technology, an adaptive filter SQP trust region algorithm. In the aspect of the trial step,we compute a quasi-normal step and a tangential step for solving the trust region subproblem,bue through Guasi-Newton method to solve the quasi-normal step.Under certain conditions, the global convergence is proved. Numerical experiments show the effectiveness of the method, and some problems in the third chapter of the algorithm is better than the result.