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Efficient hybrid conjugate gradient techniques. (English) Zbl 0666.90063
Descent properties 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 and the Polak-Ribière methods, 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 \(\beta\).
Reviewer: D.Touati-Ahmed

MSC:
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
90C52 Methods of reduced gradient type
49M37 Numerical methods based on nonlinear programming
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