On the constrained error bound condition and the projected Levenberg-Marquardt method

被引：10

作者：

Behling, R. ^{[1
]}

Fischer, A. ^{[2
]}

Haeser, G. ^{[3
]}

Ramos, A. ^{[3
]}

Schoenefeld, K. ^{[2
]}

机构：

[1] Univ Fed Santa Catarina, Dept Exact Sci, Blumenau, Brazil

[2] Tech Univ Dresden, Dept Math, Dresden, Germany

[3] Univ Sao Paulo, Inst Math & Stat, Sao Paulo, Brazil

来源：

OPTIMIZATION | 2017年 / 66卷 / 08期

基金：

巴西圣保罗研究基金会;

关键词：

Constrained equation; differentiable manifold; error bound; nonisolated solution; projected Levenberg-Marquardt method; NONISOLATED SOLUTIONS; NONLINEAR EQUATIONS; LOCAL CONVERGENCE; ALGORITHM; OPTIMIZATION; SYSTEMS;

D O I：

10.1080/02331934.2016.1200578

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：

In this paper, we first derive a characterization of the solution set of a continuously differentiable system of equations subject to a closed feasible set. Assuming that a constrained local error bound condition is satisfied, we prove that the solution set can locally be written as the intersection of a differentiable manifold with the feasible set. Based on the derivation of this result, we then show that the projected Levenberg-Marquardt method converges locally R-linearly to a possibly nonisolated solution under significantly weaker conditions than previously done.

引用

页码：1397 / 1411

页数：15

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