A PARAMETER-SELF-ADJUSTING LEVENBERG-MARQUARDT METHOD FOR SOLVING NONSMOOTH EQUATIONS

A parameter-self-adjusting Levenberg-Marquardt method (PSA-LMM) is proposed for solving a nonlinear system of equations F (x) = 0, where F : R-n -> Rn is a semismooth mapping. At each iteration, the LM parameter mu k is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA-LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.