求解半光滑方程组的LM方法收敛性分析

Levenberg-Marquardt(LM)方法是一个经典并且有效的求解非线性方程组的方法,但是目前的研究都是针对光滑方程组的.在这样的背景下,研究求解半光滑非线性方程组的LM方法.构造了求解半光滑方程组的一个参数调整LM方法(S-PALM),其中LM参数在每次迭代中是基于实际下降量和预测下降量的比值自动更新的.在水平有界的前提下,得到了S-PALM方法的全局收敛性.在强BD正则性成立的条件下,得到S-PALM方法的局部超线性收敛速度.

Convergence analysis of LM method for semismooth equations

Levenberg-Marquardt (LM) method is a classical and very efficient method for solving nonlinear equations. However, most of the references on LM method considered the smooth equations. Based on this observation, it is interesting to study the LM method for semismooth equations. A parameter-adjusting LM method for semismooth equations (S-PALM) is constructed to solve semismooth nonlinear equations, in which the parameter is updated based on the ratio between actual reduction and predicted reduction. Under level bounded condition, the global convergence of S-PALM is proved. Under strong BD regularity assumption, the local superlinear convergence rate of S-PALM is established.