A Parameter-self-adjusting Levenberg-marquardt Method for Solving Nonsmooth Equations
نویسندگان
چکیده
A parameter-self-adjusting Levenberg-Marquardt method (PSA-LMM) is proposed for solving a nonlinear system of equations F (x) = 0, where F : R → R is a semismooth mapping. At each iteration, the LM parameter μk is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSALMM 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. Mathematics subject classification: 65K05, 90C30.
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