Abstract
In this paper, by the use of Gram-Schmidt orthogonalization, we propose a class of modified conjugate gradient methods. The methods are modifications of the well-known conjugate gradient methods including the PRP, the HS, the FR and the DY methods. A common property of the modified methods is that the direction generated by any member of the class satisfies \(g_{k}^{T}d_k=-\|g_k\|^2\). Moreover, if line search is exact, the modified method reduces to the standard conjugate gradient method accordingly. In particular, we study the modified YT and YT+ methods. Under suitable conditions, we prove the global convergence of these two methods. Extensive numerical experiments show that the proposed methods are efficient for the test problems from the CUTE library.
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Supported by the NSF of China via grant 10771057.
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Cheng, W., Liu, Q. Sufficient descent nonlinear conjugate gradient methods with conjugacy condition. Numer Algor 53, 113–131 (2010). https://doi.org/10.1007/s11075-009-9318-8
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DOI: https://doi.org/10.1007/s11075-009-9318-8