一个解非光滑方程组的Levenberg-Marquardt算法

给出了一个求解非光滑约束方程组的Levenberg-Marquardt算法，每一步迭代中只需求解一个严格凸的二次规划问题．首先，利用松弛变量的绝对值函数将原问题转化成一个无约束方程组；然后，结合光滑化技术设计Levenberg—Marquardt算法．此算法具有全局收敛性，并且在弱于非奇异性的局部误差界条件下，具有局部二次收敛性质．初步的数值试验结果表明，此算法实际计算效果良好．

A Levenberg-Marquardt algorithm for solving nonsmooth equations

A new smoothing Levenberg-Marquardt algorithm was presented for solving nonsmooth constrained system of equations, which only needed to solve one strictly convex quadratic programming at each iteration. First, the original problem was converted into an unconstrained system of equations by using the absolute value function of the slack variables, then a Levenberg-Marquardt algorithm was designed by combining the smoot- hing technique. The presented algorithm converged globally, and converged locally quadratically under an error bound assumption which was much weaker than the standard nonsingularity condition. Some numerical results for the presented method indicated that the algorithm performed quite well in practice.