| Global Convergence of Conjugate Gradient Methods without Line Search |
| Received:October 27, 2017 Revised:June 06, 2018 |
| Key Words:
unconstrained optimization conjugate gradient method line search global convergence
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11761014), the Natural Science Foundation of Guangxi Zhuang Autonomous Region (Grant No.2017GXNSFAA198243), Guangxi Basic Ability Improvement Project for the Middle-Aged and Young Teachers of Colleges and Universities (Grant Nos.2017KY0068; KY2016YB069), Guangxi Higher Education Undergraduate Course Teaching Reform Project (Grant No.2017JGB147). |
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| Abstract: |
| In this paper, a new steplength formula is proposed for unconstrained optimization, which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed, and the corresponding results are as follows: (1) The DY method globally converges for a strongly convex $LC^1$ objective function; (2) The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, $LC^1$ objective function. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.05.011 |
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