Research On Algorithm For Solving Nonlinear Programming Problems

This paper studies the methods for solving general nonlinear programming (NLP) problems by a sequential quadratic programming (SQP) algorithm.We know that the SQP method generates a sequence of quadratic programming (QP) subproblems. And then, a dual quadratic programming (DQP) subproblem is generated. However, the Hessian matrix of the DQP subproblem is semidefinite, and the DQP subproblem may be unbounded or may have more solutions. In this paper we propose a modified SQP method which is based on orthogonal decomposition. In the modified method, we use orthogonal decomposition so as to delete items which lead to linear dependence of gradient in active constraints. Therefore the Hessian matrix of the DQP subproblem is positive definite. The convergence of the modified method is proved. In the last part of this paper, numerical results of the modified method are given and these results show that the modified method is effective.