| 仿射变换内点Levenberg-Marquardt法解KKT系统 |
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| 引用本文： | 王云娟,朱德通.仿射变换内点Levenberg-Marquardt法解KKT系统[J].运筹学学报,2013,17(2):89-106. |
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| 作者姓名： | 王云娟 朱德通 |
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| 作者单位： | 1. 上海立信会计学院数学与信息学院，上海 201620 2. 上海师范大学商学院， 上海 200234 |
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| 基金项目： | 国家自然科学基金 (No．10871130) |
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| 摘 要： | 提供了一类新的结合非单调内点回代线搜索技术的仿射变换Levenberg-Marquardt法解Karush-Kuhn-Tucker（KKT）系统. 基于由KKT系统转化得到的等价的部分变量具有非负约束的最小化问题，建立了Levenberg-Marquardt方程. 证明了算法不仅具有整体收敛性，而且在合理的假设条件下，算法具有超线性收敛速率. 数值结果验证了算法的实际有效性.
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| 关 键 词： | KKT系统 Levenberg-Marquardt法 仿射变换 内点 收敛 |
| 收稿时间： | 2011-03-24 |
Affine scaling interior Levenberg-Marquardt method for KKT systems |
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| WANG Yunjuan
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ZHU Detong.Affine scaling interior Levenberg-Marquardt method for KKT systems[J].OR Transactions,2013,17(2):89-106. |
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| Authors: | WANG Yunjuan ZHU Detong |
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| Affiliation: | 1. School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China 2. Business School, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | We develop and analyze a new affine scaling Levenberg-Marquardt methodwith nonmonotonic interior backtracking line search technique forsolving Karush-Kuhn-Tucker (KKT) system. By transforming the KKTsystem into an equivalent minimization problem with nonnegativity constraintson some of the variables, we establish the Levenberg-Marquardtequation based on this reformulation. Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergent rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. |
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| Keywords: | KKT systems Levenberg-Marquardt method affine scaling interior point convergence |
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