基于凸组合的列文伯格-马夸尔特算法

A levenberg-marquardt algorithm based on convex combination

在列文伯格-马夸尔特算法(L-M)在求解带非光滑约束方程组过程中,为了避免该算法受初始点和单一形式的步长影响的问题,本文采取凸组合技术(convex combination skill),将L1范数和L2范数并联使用,同时为了进一步改善L-M算法的性能,对已有的步长做出改进,提出一种新的CMLM算法,该算法每步迭代中,可以根据实际情况调整步长,并只需求解一个线性方程组.该算法全局收敛,并在局部误差界条件下,局部二次收敛.数据实验结果表明,该算法具有良好的计算效果.

In order to avoid Levenberg-Marquardt Algorithm( L-M) affected by the size of steps and initial point in solving the constraint equations of the problem,this paper adopts convex combination technique( convex combination skill),the L1 norm and L2 norm is used in parallel at the same time,in order to further improve the performance of the L-M algorithm,we present a new CMLM algorithm,which step can be adjusted according to the actual situation,and only needs to solve a linear system of equations in each iteration. The algorithm has global convergence and has local two convergence under the local error boundary condition. Preliminary numerical results show that the algorithm works well in practice.