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.
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页码：5082 / 5097
页数：16
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