A unified local convergence analysis of inexact constrained Levenberg-Marquardt methods

被引:32
作者
Behling, Roger [2 ]
Fischer, Andreas [1 ]
机构
[1] Tech Univ Dresden, Inst Numer Math, Dept Math, D-01062 Dresden, Germany
[2] Inst Nacl Matemat Pura & Aplicada, Jardim Bot, BR-22460320 Rio De Janeiro, RJ, Brazil
关键词
Constrained equation; Levenberg-Marquardt method; Convergence rate; Inexactness; Non-isolated solution; LEAST-SQUARES FORMULATION; ERROR BOUND CONDITIONS; TRUST-REGION METHODS; COMPLEMENTARITY-PROBLEMS; NONLINEAR EQUATIONS; NEWTON METHODS; ALGORITHM;
D O I
10.1007/s11590-011-0321-3
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
The Levenberg-Marquardt method is a regularized Gauss-Newton method for solving systems of nonlinear equations. If an error bound condition holds it is known that local quadratic convergence to a non-isolated solution can be achieved. This result was extended to constrained Levenberg-Marquardt methods for solving systems of equations subject to convex constraints. This paper presents a local convergence analysis for an inexact version of a constrained Levenberg-Marquardt method. It is shown that the best results known for the unconstrained case also hold for the constrained Levenberg-Marquardt method. Moreover, the influence of the regularization parameter on the level of inexactness and the convergence rate is described. The paper improves and unifies several existing results on the local convergence of Levenberg-Marquardt methods.
引用
收藏
页码:927 / 940
页数:14
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