Local convergence of quasi-Newton methods under metric regularity

被引：34

作者：

Artacho, F. J. Aragon ^{[1
]}

Belyakov, A. ^{[2
,3
]}

Dontchev, A. L. ^{[4
]}

Lopez, M. ^{[5
]}

机构：

[1] Univ Luxembourg, Syst Biochem Grp, Luxembourg Ctr Syst Biomed, L-4362 Esch Sur Alzette, Luxembourg

[2] Vienna Univ Technol, Inst Math Methods Econ, A-1040 Vienna, Austria

[3] Moscow MV Lomonosov State Univ, Inst Mech, Moscow 119192, Russia

[4] Math Reviews, Ann Arbor, MI 48107 USA

[5] Univ Alicante, Dept Stat & Operat Res, E-03080 Alicante, Spain

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2014年 / 58卷 / 01期

关键词：

Generalized equation; Quasi-Newton method; Broyden update; Strong metric subregularity; Metric regularity; Strong metric regularity; q-Superlinear convergence; SUPERLINEAR CONVERGENCE; BROYDENS METHOD;

D O I：

10.1007/s10589-013-9615-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis-Mor, condition for q-superlinear convergence. Simple numerical examples illustrate the results.

引用

页码：225 / 247

页数：23

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