Line Search Filter Methods For Solving Nonlinear Equality Constrained Optimization Problem

Nonlinear constrained optimization is widely used in many fields,such as national defense,economy,finance,engineering,management and so on.It is of great theoretical significance and practical value to construct and analyze efficient calculation methods for nonlinear constrained optimization problems.The core problem is how to balance satisfy-ing constraints and improving the value of objective function.The traditional method is to use the penalty function method which combines objectives and constraints.The recent-ly arising filter method is different from the penalty function method.The filter method avoids the difficulty of selecting penalty parameters in the penalty function method,and ensures the convergence of the algorithm.Moreover,this method has good numerical performance.In this paper,we focus on the nonlinear equality constrained optimization problem.By using a new filter,we construct a kind of line search filter algorithms and analyze the global convergence of the algorithms.The preliminary numerical results are given.In Chapter 1,the application background and mathematical model of nonlinear op-timization are summarized.The related research references are analyzed,and the main research content of this paper is introducedIn Chapter 2,for the nonlinear equality constrained optimization problem,a line search filter method is proposed.Firstly,the search direction is determined by the reduced Hessian matrix and the null space method.The optimality condition of the problem is chosen as a new filter,and then the filter technology is added to the backtracking line search framework to construct an iterative algorithm for searching the step length.Finally,the global convergence of the algorithm is proved under some reasonable assumptions,and the numerical results are given.In Chapter 3,the dwindling filter method is the improvement of the line search filter method in Chapter 2.The dwindling function is added to the step acceptable criterion,so the envelope of filter will decrease with decreasing of the step size.Therefore the step acceptable criterion is more flexible.With decreasing of the envelope,the filter will get rid of more nonstationary points,and then it reduces the storage of trial points in the iteration process.So the computational effort will be reduced.The global convergence is analyzed and the numerical results are given to show the improvement.