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第36届中国控制会议

作者： Lingxin Meng Cong Lin Xiushan Cai College of Mathematics Physics and Information Engineering Zhejiang Normal University Xingzhi College Zhejiang Normal University

ISBN: (纸本)9781538629185

Continuity of the polytope generated by a set of matrices is dealt with in this paper. We have defined a norm for the polytope, and verified when these matrices belong to a compact set in R the norm is bounded and the polytope is ***, we have verified if the polytope is treated as a set-valued mapping from R to R, it is continuous and with convex and compact values.

关键词： set-valued mappings polytopes matrices compactness continuity

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Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

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Science China Mathematics 2020年第1期63卷 39-60页

作者： Mohammed Harunor Rashid Ya-xiang Yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of Rajshahi 6205Bangladesh

Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed *** introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this ***,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this ***,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically *** example of nonsmooth functions that have p-point-based approximation is ***,a numerical experiment is given which illustrates the theoretical result.

关键词： set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation

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Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular mappings

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Applied Mathematics 2016年第11期7卷 1248-1259页

作者： Md. Asraful Alom Mohammed Harunor Rashid Kalyan Kumer Dey Department of Mathematics University of Rajshahi Rajshahi Bangladesh Department of Mathematics Faculty of Civil Engineering Khulna University of Engineering & Technology Khulna Bangladesh

We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.

关键词： set-valued mappings Metrically Regular mappings Lipschitz-Like Mapping Local and Semi-Local Convergence

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Modification of the Convergence of GG-PPA for Solving Generalized Equations

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Journal of Applied Mathematics and Physics 2023年第1期11卷 260-275页

作者： Asraful Alom Zaidur Rahman Bayezid Gazi Imran Hossain Department of Mathematics Khulna University of Engineering & Technology Khulna Bangladesh

A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 ∈T(x), where T is a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show the existence of any sequence generated by the modified GG-PPA and prove the semi-local and local convergence results by using metrically regular mapping. In addition, we give a numerical example to justify the result of semi-local convergence.

关键词： set-valued mappings Metrically Regular mappings Semi-Local Convergence Lipschitz Continuous Fixed Point Lemma

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