A new superlinearly convergent algorithm of combining QP subproblem with system of linear equations for nonlinear optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:273

Article

Jian, Jin-Bao¹  Guo, Chuan-Hao²  Tang, Chun-Ming³  Bai, Yan-Qin⁴ 

[1] Yulin Normal Univ, Sch Math & Informat Sci, Yulin 537000, Peoples R China

[2] Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China

[3] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China

[4] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

关键词: Nonlinear optimization;    Sequential quadratic programming;    Method of strongly sub-feasible directions;    Global convergence;    Superlinear convergence;   

DOI  :  10.1016/j.cam.2014.06.009

来源: Elsevier

【 摘 要 】

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly convergent algorithm is proposed. The initial iteration point can be chosen arbitrarily for the algorithm. At each iteration, the new algorithm solves one quadratic programming subproblem which is always feasible, and one or two systems of linear equations with a common coefficient matrix. Moreover, the coefficient matrix is uniformly nonsingular. After finite iterations, the iteration points can always enter the feasible set of the problem, and the search direction is obtained by solving one quadratic programming subproblem and only one system of linear equations. The new algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some numerical results are reported to show that the algorithm is promising. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free