| 一个新的SQP方法及其超线性收敛性 |
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| 引用本文： | 张菊亮,王长钰.一个新的SQP方法及其超线性收敛性[J].运筹学学报,2000,4(2):32-40. |
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| 作者姓名： | 张菊亮 王长钰 |
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| 作者单位： | 1. 中国科学院应用数学研究所,北京,100080
2. 曲阜师范大学运筹学所,山东曲阜,273165 |
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| 基金项目： | the National Natural Science Foundation of China (Grant No. 19871049). |
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| 摘 要： | 由Ｗｉｌｓｏｎ，Ｈａｎ，Ｐｏｗｅｌｌ发展的ＳＱＰ技术是解非线性规划的最有效的方法之一，但是，如果其中的二次子规划问题无可行解或者其搜索方向向量无界，该方法ａｎ和Ｂｕｒｋｅ「３」，周广路「２」分别对二次规划问题作了修正，克服了上述矛盾，本文在「２」的基础上，进上步修正，证明在Ａｒｍｉｊｏ搜索下算法具有全局收敛性，并通过解一辅助线性方程组，利用弧式搜索，得出该方法具有超线性收敛性。
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| 关 键 词： | 修正SQP方法 非线性规划 二次规划 超线性收敛性 |
| 修稿时间： | 1999-03-15 |
A Modified SQP Method and Its Superlinear Convergence |
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| JULIANG ZHANG,CHANGYU WANG.A Modified SQP Method and Its Superlinear Convergence[J].OR Transactions,2000,4(2):32-40. |
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| Authors: | JULIANG ZHANG CHANGYU WANG |
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| Institution: | JULIANG ZHANG
(Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080)CHANGYU WANG
(Institute of Operation Research, Qufu Normal University, Qufu, Shangdong, 273165) |
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| Abstract: | The SQP technique developed by Wilson, Had and Powell is one of the most effective algorithms for solving nonlinear mathematical programming. However, the method fails if the quadratic subproblem is infeasible or the search direction is unbounded. Han and Burke3], G.L.Zhou2] have modified the quadrant subproblem respectively and overcome the difficulty. In this paper, we modify the algorithm in 2] further and prove that the algorithm is globally convergent under Armijo linesearch. Moreover, we use the second- order correction, which is obtained by solving an auxiliary linear equation system, and arc-search to obtain the superlinear convergence of the algorithm. |
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| Keywords: | modified SQP method Armjo search global convergence superlinear convergence |
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