| 一个修正的秩1拟牛顿法及其收敛性质 |
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| 引用本文： | 吴士泉(),高自友(). 一个修正的秩1拟牛顿法及其收敛性质[J]. 系统科学与数学, 1988, 8(4): 373-380 |
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| 作者姓名： | 吴士泉() 高自友() |
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| 作者单位： | 中国科学院应用数学研究所(吴士泉)，山东矿业学院(高自友) |
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| 摘 要： | 的拟牛顿算法,具有结构简单,易于实现的特点.当用于正定二次凸函数时,算法有较好的收敛性质.但是,它也有严重的缺点.一方面,即使 H_k 正定,也不能保证 H_(k+1) 是正定的;另一方面,(S_k—H_kYk)~TY_k 可能为0,这时算法就不再有定义.自从秩1拟牛顿法问世以来,许多学者都想将其改变为一个有用的算法(参见),
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A MODIFIED RANK-ONE QUASI-NEWTON METHOD AND ITS CONVERGENCE PROPERTIES |
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| WU SHI-QUAN,GAO ZI-YOU. A MODIFIED RANK-ONE QUASI-NEWTON METHOD AND ITS CONVERGENCE PROPERTIES[J]. Journal of Systems Science and Mathematical Sciences, 1988, 8(4): 373-380 |
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| Authors: | WU SHI-QUAN GAO ZI-YOU |
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| Affiliation: | (1)Institute of Applied Mathematics,Academia Sinica;(2)Shandong Mining Institute |
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| Abstract: | The rank-one quasi-Newton method has fatal defects,it can not gurantee that H_k is positivedefinite and (H_k-H_kY_k)~TY_k is not zero.When these cases occur,the method is notdefined.In this paper we overcome all these shortcomings by revising the rank-one method.Under weak conditions we prove that our new method is quadratically terminated and hasstrong convergence properties when applied to quadratic functions and general continuouslydifferentiable functions respectively. |
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