Nonsmooth Bundle Trust-region Algorithm with Applications to Robust Stability

被引：19

作者：

Apkarian, Pierre ^{[1
]}

Noll, Dominikus ^{[2
]}

Ravanbod, Laleh ^{[2
]}

机构：

[1] Off Natl Etud & Rech Aerosp, Control Syst Dept, Toulouse, France

[2] Univ Toulouse, Inst Math, Toulouse, France

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2016年 / 24卷 / 01期

关键词：

Bundle; Cutting plane; Trust-region; Cauchy point; Global convergence; Parametric robustness; Distance to instability; Worst-case H-infinity-norm; PROXIMITY CONTROL ALGORITHM; GLOBAL OPTIMIZATION; MINIMIZE NONSMOOTH; DESCENT METHODS; CONVERGENCE; POLYNOMIALS; SMOOTH;

D O I：

10.1007/s11228-015-0352-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a bundle trust-region algorithm to minimize locally Lipschitz functions which are potentially nonsmooth and nonconvex. We prove global convergence of our method and show by way of an example that the classical convergence argument in trust-region methods based on the Cauchy point fails in the nonsmooth setting. Our method is tested experimentally on three problems in automatic control.

引用

页码：115 / 148

页数：34

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