MODIFIED SPECTRAL CONJUGATE GRADIENT METHODS BASED ON THE QUASI-NEWTON ASPECTS

摘要

A class of spectral conjugate gradient methods is developed for solving unconstrained optimization problems in which the conjugate gradient parameter is computed based on the quasi Newton aspects and then, the spectral parameter is determined to improve condition number of the corresponding search direction matrix. The given conjugate gradient parameter can be considered as a two parameter extension of the Dai-Liao conjugate gradient parameter. To achieve sufficient descent property, a three term extension of the given class of conjugate gradient methods is developed. Global convergence analysis of the methods is conducted. Numerical experiments are done on a set of test problems of the CUTEr collection. They show practical efficiency of the given adaptive choices of the parameters in the sense of the Dolan-More performance profile.