Extended Newton-type method for nonlinear functions with values in a cone

被引：1

作者：

Silva, G. N. ^{[1
]}

Santos, P. S. M. ^{[2
]}

Souza, S. S. ^{[2
]}

机构：

[1] Univ Fed Oeste Bahia, Ctr Ciencias Exatas & Tecnol, BR-47808021 Barreiras, BA, Brazil

[2] Univ Fed Piaui, Dept Matemat, Parnaiba, PI, Brazil

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 04期

关键词：

Newton-like method; Inclusion problem; Banach space; Convex process; CONVEX-COMPOSITE OPTIMIZATION; SOLVING GENERALIZED EQUATIONS; MAJORANT CONDITION; CONVERGENCE ANALYSIS; INCLUSION PROBLEMS; OUTER INVERSES; BANACH-SPACES; ERROR-BOUNDS; KANTOROVICHS; INEQUALITIES;

D O I：

10.1007/s40314-018-0617-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341-347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295-313, 1986; Numer Math 51(5):545-557, 1987) and Robinson (Numer Math 19:341-347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results.

引用

页码：5082 / 5097

页数：16

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