Efficient hybrid conjugate gradient techniques

Abstract

Descent property and global convergence proofs are given for a new hybrid conjugate gradient algorithm. Computational results for this algorithm are also given and compared with those of the Fletcher-Reeves method and the Polak-Ribiere method, showing a considerable improvement over the latter two methods. We also give new criteria for restarting conjugate gradient algorithms that prove to be computationally very efficient. These criteria provide a descent property and global convergence for any conjugate gradient algorithm using a nonnegative update β.