AN ALGORITHM OF SEQUENTIAL SYSTEMS OF LINEAR-EQUATIONS FOR NONLINEAR OPTIMIZATION PROBLEMS WITH ARBITRARY INITIAL POINT

For current sequential quadratic programming (SQP) type algorithms, th ere exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteratio n, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithm s require that the related quadratic programming subproblems be solvab le per iteration, hut it is difficult to be satisfied. By using e-acti ve set procedure with a special penalty function as the merit function , a new algorithm oi sequential systems of linear equations for genera l nonlinear optimization problems with arbitrary initial point is pres ented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has gl obal convergence and local superlinear convergence: To some extent, th e new algorithm can overcome the shortcomings of the SQP algorithms me ntioned above.