| 非线性最优化中超线性收敛的序列线性方程组方法 |
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| 引用本文： | 高自友,吴方,赖炎连.非线性最优化中超线性收敛的序列线性方程组方法[J].北京交通大学学报(自然科学版),1995(4). |
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| 作者姓名： | 高自友 吴方 赖炎连 |
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| 作者单位： | 北方交通大学运输系统模拟中心，中国科学院应用数学研究所 |
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| 摘 要： | 提出了一个超线性收敛的序列线性方程组方法（ＳＳＬＥ）．此方法与现有的序列二次规划（ＳＱＰ）方法相比，其优点有：（１）由于新方法每一次迭代只需计算三个系数矩阵完全相同的线性方程组，因此迭代的计算量减少且算法的稳定性提高；（２）每一次迭代产生的点是可行的；（３）具有一步超线性收敛速度。
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| 关 键 词： | 最优化，线性方程组，收敛性质 |
Superlinear Convergent Algorithm of Linear Sequential Equations for Nonlinear Optimization Problems |
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| Gao Ziyou.Superlinear Convergent Algorithm of Linear Sequential Equations for Nonlinear Optimization Problems[J].JOURNAL OF BEIJING JIAOTONG UNIVERSITY,1995(4). |
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| Authors: | Gao Ziyou |
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| Abstract: | In this paper, a new superlinearly convergent algorithm of sequential linear equations (SSLE) for nonlinear optimization problems with nonlinear constraints is proposed. Comparing with the existing algorithms of Sequential Quadratic Programming ( SQP) , the new algorithm has three main advantages, i. e., (1) Since the new algorithm needs only to solve three systems of linear equations having the same coefficient matrix in each iteration, the computation amount of the algorithm is much less than that of the existing ones;(2) The iteration points generated by the algorithm are feasible;(3) The new algorithm is globally convergent and the rate of convergence of the new algorithm is one-step superliner. |
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| Keywords: | ss: optimization systems of linear equations convergence |
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