An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point  

作　　者：高自友 贺国平 吴方 

机构地区：[1]Northern Jiaotong University, Beijing 100044, China [2]Shandong Institute of Mining and Technology, Taian 271019, China [3]Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Science China Mathematics》1997年第6期561-571,共11页中国科学：数学（英文版）

基　　金：Project partly supported by the National Natural Science Foundation of China and Tianyuan Foundation of China.

摘　　要：For current sequential quadratic programming (SQP) type algorithms, there exist two problems; (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.For current sequential quadratic programming (SQP) type algorithms, there exist two problems; (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.

关 键 词：constrained optimization problem ALGORITHM of SEQUENTIAL systems of linear EQUATIONS SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM convergence. 

分 类 号：O224[理学—运筹学与控制论]