Smoothing Newton Method For Nonlinear Programming Problem And Sqp-filter Method For Constrained Minimax Problem

In this thesis, we discuss Smoothing Newton Method for Nonlinear Programming Problem and SQP-Filter Method for constrained Min-max Problem.In Chapter 1, a new smoothing Newton Method is proposed for solving equality and inequality constrained nonlinear programming problem. This method is based on Smoothing min-function, by KKT optimality conditions, Original constrained optimization problem is converted into the solution of equivalent smoothing equation set. And, the proposed algorithm is proved to be well-defined and convergent globally under weaker conditions.Numerical experiments show the method is effective.SQP Method is a most effective way to solve constrained nonlinear programming problem,but it is difficult to electing the penalty factor, Filter skill can avoid it.So,In Chapter 2, a SQP-Filter Method is proposed for solving equality and inequality constrained Minimax problem.Each time by solving the second sub-programming to get the search direction, and along the direction for line search. This method avoids the difficult problem of selecting the penalty factor, and overcomes Maratos effects successfully.Its global and super-linear convergence are obtained under some suitable conditions.Last, we make a conclusion of the work. In this section, we simply introduce research progress and achievement of the subject, and point out the problem need to be solved.