Two effective hybrid conjugate gradient algorithms based on modified BFGS updates |
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Authors: | Saman Babaie-Kafaki Masoud Fatemi Nezam Mahdavi-Amiri |
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Institution: | (3) Center for Advanced Modeling and Optimization, Research Institute for Informatics, Bucharest, Romania;(4) Academy of Romanian Scientists, Bucharest, Romania; |
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Abstract: | Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei,
and introduce two hybrid conjugate gradient methods for unconstrained optimization problems. Our methods are hybridizations
of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. Under proper conditions, we show that one of the proposed algorithms
is globally convergent for uniformly convex functions and the other is globally convergent for general functions. To enhance
the performance of the line search procedure, we propose a new approach for computing the initial value of the steplength
for initiating the line search procedure. We give a comparison of the implementations of our algorithms with two efficiently
representative hybrid conjugate gradient methods proposed by Andrei using unconstrained optimization test problems from the
CUTEr collection. Numerical results show that, in the sense of the performance profile introduced by Dolan and Moré, the proposed
hybrid algorithms are competitive, and in some cases more efficient. |
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Keywords: | |
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