LEVENBERG-MARQUARDT METHOD WITH A GENERAL LM PARAMETER AND A NONMONOTONE TRUST REGION TECHNIQUE

We propose a new Levenb erg -Marquardt (LM) method for solving the nonlinear equations. The new LM method takes a general LM parameter lambda k = mu k [(1 - 0 ) IF k I delta + 0 IIJ kT F k e ] where 0 is an element of [0 , 1] and delta is an element of (0 , 3) and adopts a nonmonotone trust region technique to ensure the global convergence. Under the local error bound condition, we prove that the new LM method has at least a superlinear convergence rate with the order min { 1 + delta, 4 - delta, 2 } . We also apply the new LM method to solve the nonlinear equations arising from the weighted linear complementarity problem. Numerical experiments indicate that the new LM method is efficient and promising.