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| 超线性与二次收敛的序列方程组可行方法 | |
| 引用本文： | 简金宝,赖炎连,张可村. 超线性与二次收敛的序列方程组可行方法[J]. 数学学报, 2002, 45(6): 1137-114. DOI: cnki:ISSN:0583-1431.0.2002-06-012 |
| 作者姓名： | 简金宝 赖炎连 张可村 |
| 作者单位： | 1. 广西大学数学与信息科学系,广西,南宁,530004 2. 中国科学院数学与系统科学研究院应用数学研究所,北京,100080 3. 西安交通大学理学院,陕西,西安,710049 |
| 基金项目： | 国家自然科学基金（19801009），广西自然科学基金（9811023），桂料基（0236001）资助项目 |
| 摘 要： | 本文讨论不等式约束规划问题,给出一个线性方程组与辅助方向相结合的新可行算法,算法用一种新型的直线搜索产生步长.在一定条件下,当k充分大后,求方向dk每次只需解一个线性方程组.文中证明了算法的全局收敛性与超线性的收敛速度以及二次收敛性,并给出了方法初步的数值试验. |
| 关 键 词： | 不等式约束 非线性规划 序列方程组 可行方法 超线性与二次收敛性 |
| 文章编号： | 0583-1431(2002)06-1137-10 |
| 修稿时间： | 1999-05-04 |
A Feasible Method for Superlinearly and Quadratically Convergent Sequential Systems of Equations |
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| Jin Bao JIAN. A Feasible Method for Superlinearly and Quadratically Convergent Sequential Systems of Equations[J]. Acta Mathematica Sinica, 2002, 45(6): 1137-114. DOI: cnki:ISSN:0583-1431.0.2002-06-012 | |
| Authors: | Jin Bao JIAN |
| Affiliation: | Jin Bao JIAN(Department of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China)Yan Lian LAI(Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. C |
| Abstract: | Abstract In this paper, inequality constrained programming problems are discussed, based on a combination technique of a system of linear equations and an auxiliary direction, a new feasible algorithm is presented, where the step size is found by a new line search. Under suitable conditions, only one system of linear equations needs to be solved for finding the direction dk when k is large enough. The algorithm isproved to possess global convergence, rate of superlinear convergence and quadratical convergence. Some preliminary numerical results are reported. |
| Keywords: | Inequality constraints Nonlinear programming Sequential system of equa-tions Superlinear and quadratical convergence |
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