A CLASS OF DESCENT FOUR-TERM EXTENSION OF THE DAI-LIAO CONJUGATE GRADIENT METHOD BASED ON THE SCALED MEMORYLESS BFGS UPDATE

摘要

Hybridizing the three-term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Dai and Liao based on the scaled memoryless BFGS update, a one-parameter class of four-term conjugate gradient methods is proposed. It is shown that the suggested class of conjugate gradient methods possesses the sufficient descent property, without convexity assumption on the objective function. A brief global convergence analysis is made for uniformly convex objective functions. Results of numerical comparisons are reported. They demonstrate efficiency of a method of the proposed class in the sense of the Dolan-More performance profile.