| ON THE CONVERGENCE OF MULTIPLICATIVE ITERATIVE ALGORITHMS WITH INEXACT LINE SEARCH |
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| 引用本文： | 杨晓光. ON THE CONVERGENCE OF MULTIPLICATIVE ITERATIVE ALGORITHMS WITH INEXACT LINE SEARCH[J]. 应用数学学报(英文版), 1997, 13(4): 337-341. DOI: 10.1007/BF02009541 |
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| 作者姓名： | 杨晓光 |
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| 作者单位： | Institute of Systems Science. the Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | 1.IntroductionIntillspaperweanalyzetheconvergenceonmultiplicativeiterativealgorithmsfortheIninimizationofadiffcrentiablefunctiondefinedonthepositiveorthantofR".ThealgorithmissllggestedbyEggermolltl'],andisrelatedtotheEM[2](Expextation--Maximization)algoritllnlforPositronemissiontonlography[']andimagereconstructi..14].Wecollsidertheproblenl"linf(x)s.t.x20.Themultiplicativeiterativealgorithmshavethel'orlniforj=l,2,',n,withAhdeterminedthroughalinesearch.Whilelusem[5]establishedanelegantconv…
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| 收稿时间： | 1993-12-02 |
On the convergence of multiplicative iterative algorithms with inexact line search |
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| Xiaoguang Yang. On the convergence of multiplicative iterative algorithms with inexact line search[J]. Acta Mathematicae Applicatae Sinica, 1997, 13(4): 337-341. DOI: 10.1007/BF02009541 |
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| Authors: | Xiaoguang Yang |
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| Affiliation: | (1) Institute of Systems Science, the Chinese Academy of Sciences, 100080 Beijing, China |
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| Abstract: | This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assumption of convexity of objective function or the assumption of convergence of the sequence generated by the algorithm. This answers an open problem put forward by lusem. |
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| Keywords: | Multipl icative iterative algorithm inexact line search convergence |
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