Global Convergence of Conjugate Gradient Methods without Line Search |
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Authors: | Jie Sun Jiapu Zhang |
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Institution: | (1) Department of Decision Sciences, National University of Singapore, Republic of Singapore;(2) Department of Mathematics, University of Melbourne, Melbourne, Australia |
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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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Keywords: | conjugate gradient methods convergence of algorithms line search |
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