A Modified Quasi-Newton Algorithm For Inequality Constrained Optimization

We are concerned in the inequality constrained nonlinear programming problems in this paper. Nonlinear programming is a most important branch of operational research. While the inequality constrained optimization is a special situation of nonlinear programming. Because of its good convergence and stability, the truncated Newton method is concerned as an important method for nonlinear programming, and is used broadly in many domains.There are six parts in this paper. In Chapter 1, we introduce the inequality constrained optimization and its development. In Chapter 2, we introduce quasi-Newton method and modified Newton method.We propose a modified quasi-Newton algorithm in Chapters 3. In this algorithm, an exact penalty function is chosen as the merit function, without using the second order information, the search direction is determined by solving a subproblem. Compared with the multiplier method, this algorithm is a litter superior in the computation and its efficiency, and can be used for sparse large scale problems. We prove its global convergence in Chapter 4, and give some numerical examples in Chapter 5. The numerical tests show that the modified quasi-Newton algorithm is promising.