A variant spectral-type FR conjugate gradient method and its global convergence

摘要

In this paper, we propose a variant FR (VFR) formula β_kVFR and corresponding spectral-type conjugate gradient method (SVFR) such that the direction generated is always a descent direction for the objective function. We also extend β_k~(VFR) to βk* such that |β_k*|≤β_k~(FR) and have similar conclusions. Under appropriate conditions, we prove that the proposed method is globally convergent under not only Wolfe line search but also Armijo-type line search. Numerical experiments show the SVFR method performs well.