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| AN OPTIMAL SELF-SCALING STRATEGY TO THE MODIFIED SYMMETRIC RANK ONE UPDATING | |
| 引用本文： | 杨月婷 徐成贤 高岳林. AN OPTIMAL SELF-SCALING STRATEGY TO THE MODIFIED SYMMETRIC RANK ONE UPDATING[J]. 西安交通大学学报(英文版), 2005, 17(1): 1-5 |
| 作者姓名： | 杨月婷 徐成贤 高岳林 |
| 作者单位： | Faculty of Sciences，Xi'an Jiaotong University，Faculty of Sciences，Xi'an Jiaotong University，Department of Information and Computation Science，the Second Northwest Institute for Ethnic Minorities Xi'an 710049，China，Department of Mathematics，Beihua University，Jilin132013，China，Xi'an 710049，China，Yinchuan750021，China. |
| 基金项目： | ThisworkwassupportedbytheNationalNaturalScienceFoundationofChina(No.10231060) |
| 摘 要： | 1 Introduction Inthispaper,weconsidertheunconstrained optimizationproblem minf(x)(1.1) wheref(x):Rn→Ristwicecontinuouslydifferen tiable,andasolutionx totheproblemexists.Qua si Newtonmethodsforsolvingproblem(1.1)are widelyapplied.Startingfromaninitialpo… |
| 关 键 词： | 无约束最优化 HSR1 准牛顿方程 对称序列 |
AN OPTIMAL SELF-SCALING STRATEGY TO THE MODIFIED SYMMETRIC RANK ONE UPDATING |
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| Yang Yueting,Xu Chengxian,Gao Yuelin. AN OPTIMAL SELF-SCALING STRATEGY TO THE MODIFIED SYMMETRIC RANK ONE UPDATING[J]. Academic Journal of Xi’an Jiaotong University, 2005, 17(1): 1-5 | |
| Authors: | Yang Yueting Xu Chengxian Gao Yuelin |
| Affiliation: | 1. Department of Mathematics, Beihua University, Jilin 132013, China 2. Faculty of Sciences, Xi'an Jiaotong University, Xi'an 710049, China 3. Department of Information and Computation Science, the Second Northwest Institute for Ethnic Minorities, Yinchuan 750021, China |
| Abstract: | In the paper, the optimal self-scaling strategy to the modified symmetric rank one (HSR1) update, which satisfies the modified quasi-Newton equation, is derived to improve the condition number of the updates. The scaling factors are derived from minimizing the estimate of upper bounds on the condition number of the updating matrix. Theoretical analysis, and numerical experiments and comparisons show that introducing the optimal scaling factor into the modified symmetric rank one update preserves the positive definiteness of updates, and greatly improves the stability and numerical performance of the modified symmetric rank one algorithm. |
| Keywords: | unconstrained optimization modified quasi-Newton equation SR1 update |
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