Levenberg-Marquardt算法
数学
非线性系统
应用数学
数学优化
趋同(经济学)
正多边形
非线性规划
计算机科学
凸优化
牛顿法
收敛速度
出处
期刊:Journal of Industrial and Management Optimization
[American Institute of Mathematical Sciences]
日期:2012-12-01
卷期号:9 (1): 227-241
被引量:20
标识
DOI:10.3934/jimo.2013.9.227
摘要
In this paper, both the constrained Levenberg-Marquardt method and the projected Levenberg-Marquardt method
are presented for nonlinear equations $F(x)=0$ subject to $x\in X$, where $X$ is a nonempty closed convex set.
The Levenberg-Marquardt parameter is taken as $\| F(x_k) \|_2^\delta$ with $\delta\in (0, 2]$.
Under the local error bound condition which is weaker than nonsingularity,
the methods are shown to have the same convergence rate,
which includes not only the convergence results obtained in [12] for $\delta=2$
but also the results given in [7] for unconstrained nonlinear equations.
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