Extended Semismooth Newton Method for Functions with Values in a Cone

被引：2
|
作者：
Bernard, Severine [1 ]
Cabuzel, Catherine [1 ]
Nuiro, Silvere Paul [1 ]
Pietrus, Alain [1 ]
机构：
[1] Univ Antilles, Dept Math & Informat, Lab LAMIA, EA 4540, Campus Fouillole, F-97159 Pointe a Pitre, Guadeloupe, France
来源：
ACTA APPLICANDAE MATHEMATICAE | 2018年 / 155卷 / 01期
关键词：
Variational inclusion; Semismooth function; Closed convex cone; Majorizing sequence; Normed convex process; GENERALIZED EQUATIONS; LOCAL CONVERGENCE; CONVEX; 2ND-ORDER;
D O I：
10.1007/s10440-017-0146-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with variational inclusions of the form 0 is an element of K - f(x)where f : R-n -> R-m is a semismooth function and is a nonempty closed convex cone in R-n. We show that the previous problem can be solved by a Newton-type method using the Clarke generalized Jacobian of . The results obtained in this paper extend those obtained by Robinson in the famous paper (Robinson in Numer. Math. 19:341-347, 1972). We provide a semilocal method with a superlinear convergence that is new in the context of semismooth functions. Finally, numerical results are also given to illustrate the convergence.
引用
收藏
页码：85 / 98
页数：14
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