Abstract
Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC 1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC 1 objective function.
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Sun, J., Zhang, J. Global Convergence of Conjugate Gradient Methods without Line Search. Annals of Operations Research 103, 161–173 (2001). https://doi.org/10.1023/A:1012903105391
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DOI: https://doi.org/10.1023/A:1012903105391