Convergence of a two-parameter family of conjugate gradient methods with a fixed formula of stepsize
Abstract
We prove the global convergence of a two-parameter family of conjugate gradient methods that use a new and different formula of stepsize from Wu \cite%
{14}. Numerical results are presented to confirm the effectiveness of the proposed stepsizes by comparing with the stepsizes suggested by Sun and his colleagues \cite% {2, 12}.\\
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References
N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim, 10(1), 147–161, (2008).
X. Chen and J. Sun, Global convergence of a two-parameter family of conjugate gradient methods without line search, Journal of Computational and Applied Mathematics, 146(1),37– 45, (2002).
Y. Dai and Y. Yuan, A three-parameter family of nonlinear conjugate gradient methods, Mathematics of Computation, 70(235), 1155–1167, (2001).
Y.H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM Journal on Optimization, 10(1), 177–182, (1999).
R. Fletcher, Practical methods of optimization, John Wiley & Sons, (1987).
R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, The computer journal, 7(2), 149–154, (1964).
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, volume 49. NBS, (1952).
Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, Journal of Optimization Theory and Applications, 69(1), 129–137, (1991).
J. More and E. D. Dolan, Benchmarking optimization software with performance files, Math. Program, 91(2), 2001-2013, (2002).
B. T. Polyak, The conjugate gradient method in extremal problems, USSR Computational Mathematics and Mathematical Physics, 9(4), 94–112, (1969).
B. Sellami Y. Laskri and R. Benzine, A new two-parameter family of nonlinear conjugate gradient methods, Optimization, 64 (4) , 993–1009, (2015).
J. Sun and J. Zhang, Global convergence of conjugate gradient methods without line search, Annals of Operations Research, 103(1-4), 161–173, (2001).
P. Wolfe, Convergence conditions for ascent methods, ii: Some corrections. SIAM review, 13(2), 185–188, (1971).
Q.-j. Wu, A nonlinear conjugate gradient method without line search and its global convergence, In Computational and Information Sciences (ICCIS), 2011 International Conference on. IEEE, 1148–1152, (2011).
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