On the convergence of the modified Levenberg-Marquardt method with a nonmonotone second order Armijo type line search

Recently, Fan [4, Math. Comput., 81 (2012), pp. 447-466] proposed a modified Levenberg-Marquardt (MLM) method for nonlinear equations. Using a trust region technique, global and cubic convergence of the MLM method is proved [4] under the local error bound condition, which is weaker than nonsingularity. The purpose of the paper is to investigate the convergence … Read more

A globally and R-linearly convergent hybrid HS and PRP method and its inexact version with applications

A hybrid HS and PRP type conjugate gradient method for smooth optimization is presented, which reduces to the classical RPR or HS method if exact linear search is used and converges globally and R-linearly for nonconvex functions with an inexact backtracking line search under standard assumption. An inexact version of the proposed method which admits … Read more

A short note on the global convergence of the unmodified PRP method

It is well-known that the search direction generated by the standard (unmodified) PRP nonlinear conjugate gradient method is not necessarily a descent direction of the objective function, which brings difficulty for its global convergence for general functions. However, to our surprise, it is easily proved in this short note that the unmodified PRP method still … Read more