Affine scaling interior Levenberg-Marquardt method for bound-constrained semismooth equations under local error bound conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:219

Article

Zhu, Detong

关键词: semismooth equation;    Levenberg-Marquardt method;    affine scaling;    interior point;    superlinear convergence;    error bounds;   

DOI  :  10.1016/j.cam.2007.07.039

来源: Elsevier

【 摘 要 】

We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving hound-constrained semismooth equations under local error bound conditions. The affine scaling Levenberg-Marquardt equation is based on a minimization of the squared Euclidean norm of linear model adding a quadratic affine scaling matrix to find a Solution that belongs to the bounded constraints on variable. The global convergence results are developed in a very general setting of computing trial directions by a semismooth Levenberg-Marquardt method where a backtracking line search technique projects trial steps onto the feasible interior set. We establish that close to the solution set the affine scaling interior Levenberg-Marquardt algorithm is shown to converge locally Q-superlinearly depending on the quality of the semismooth and Levenberg-Marquardt parameter under an error bound assumption that is Much weaker than the standard nonsingularity condition, that is, BD-regular condition under nonsmooth case. A nonmonotonic criterion should bring about speed up the convergence progress in the contours of objective function with large curvature. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free