| Newton type methods for solving nonsmooth equations |
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| 引用本文： | Gao YanSchool of Management,Univ. of Shanghai for Science and Technology,Shanghai 200093,P. R. China. Newton type methods for solving nonsmooth equations[J]. 系统工程与电子技术(英文版), 2005, 16(4) |
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| 作者姓名： | Gao YanSchool of Management Univ. of Shanghai for Science and Technology Shanghai 200093 P. R. China |
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| 作者单位： | Gao YanSchool of Management，Univ. of Shanghai for Science and Technology，Shanghai 200093，P. R. China |
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| 摘 要： | 1.INTRODUCTION Thenonsmoothequationsproblemplaysanimportant roleinengineering,systemanalysis,management scienceandetc.Manypublicationsdealtwiththe methodsforsolutionofnonsmoothequations,see Refs.[1～4].Letusconsiderthesystemofnons moothequations F(x)=0(1)whereF∶Rn→RmislocallyLipschitzian.NewtonmethodsforsolvingthenonsmoothEq.(1)aregiven asfollows xk+1=xk-V-1kF(xk)(2)whereVkisanelementofvarioussubdifferentialsof Fatxk,forinstance,Clarkesubdifferential[1],B differential[2],b differen…
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Newton type methods for solving nonsmooth equations |
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| Gao Yan. Newton type methods for solving nonsmooth equations[J]. Journal of Systems Engineering and Electronics, 2005, 16(4) |
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| Authors: | Gao Yan |
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| Affiliation: | School of Management, Univ. of Shanghai for Science and Technology, Shanghai 200093, P. R. China |
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| Abstract: | Numerical methods for the solution of nonsmooth equations are studied. A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods for solving nonsmooth equations are developed and their convergence is shown. Since this subdifferential is easy to be computed, the present Newton methods can be executed easily in some applications. |
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| Keywords: | nonsmooth equations newton methods subdifferential nonsmooth optimization. |
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