Tame functions are semismooth

被引：39

作者：

Bolte, Jerome ^{[1
]}

Daniilidis, Aris ^{[3
]}

Lewis, Adrian ^{[2
]}

机构：

[1] Univ Paris 06, Equipe Combinatoire & Optimisat, Case 189, F-75252 Paris 05, France

[2] Cornell Univ, Sch ORIE, Ithaca, NY 14853 USA

[3] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

来源：

MATHEMATICAL PROGRAMMING | 2009年 / 117卷 / 1-2期

关键词：

semismoothness; semi-algebraic function; o-minimal structure; nonsmooth Newton method; structured optimization problem; superlinear convergence; O-MINIMAL STRUCTURES;

D O I：

10.1007/s10107-007-0166-9

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Superlinear convergence of the Newton method for nonsmooth equations requires a "semismoothness" assumption. In this work we prove that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebraic, or more generally, globally subanalytic mappings present the special interest of being gamma-order semismooth, where gamma is a positive parameter. As an application of this new estimate, we prove that the error at the kth step of the Newton method behaves like O(2(-(1+gamma)k)).

引用

页码：5 / 19

页数：15

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