Sequential Systems Of Linear Equations Algorithm For Nonlinear Optimization Problems - Inequality Constrained Problems
Zi You Gao 1, Tian De Guo 2, Guo Ping He 3, Fang Wu 31 School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, China
2 Institute for Loo-Keng Hua Applied Mathematics and Information Sciences, Graduate School of Chinese Academy of Sciences, Beijing 100039, China
3 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 10080, China
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations gaving a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration.Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic qrogramming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the relatrd systems of linear equations always have solutions. Some numerical results are reported.
Key words: Optimization; Inequality constraints; Algorithms; Sequential systems of linear equations; Coefficient matrices.