ENHANCE THE EFFICIENCY OF RMIL'S FORMULA FOR MINIMUM PROBLEM
In this paper, a new formula of is suggested for conjugate gradient method of solving unconstrained optimization problems based on depends on the creation and update of RMIL’S formula with the inclusion of a parameter and step size of cubic. Our novel proposed CG-method has descent condition and global convergence properties. Numerical comparisons with standard conjugate gradient algorithm of RMIL’S formula show that this algorithm very effective depending on the number of iterations and the number of functions evaluation.
Dixon, L. G. W., Conjugate Gradient Algorithms Quadratic Termination Without Linear Searches, Journal of Inst. of Mathematics And its Applications, (15) (1975), 9-15.
E. Polak and G. Ribiere, Note sur la convergence de directionsconjugees, Rev. Francaise Informat Recherche Operationelle. 3E Annee, (16) (1969), 35-43.
H. Ageel KH, S. Gazi SH, A New conjugate gradient method for unconstrained optimization problems with descent property, General Letters in Mathematics, 9(2) (2020), 39 -44.
I. Mohammed S., M. Mamat, K. Kamfa, M. Danlami, A Descent Modification of Conjugate Gradient Method for Optimizatio Models, Iraqi Journal of Science, 61 (7) (2020), 1745-1750.
M. B. Yousef, M. Mamat and M. Rivaie, A New Modification of Conjugate Gradient Method with Global Convergence and Sufficient Descent Properties for Unconstrained Optimization Problems, ASM Science Journal, 12(6) (2019).
M. Rivaie, M. Mamat, L. W. June and I. Mohd, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Applied Mathematics and Computation, 218 (2012), 11323-11332.
M. Rivaie, M. Mamat, L. W. June and I. Mohd, A new conjugate gradient coefficient for large scale nonlinear unconstrained optimization, International Journal of Mathematical Analysis, 23(6) (2012),1131-1146.
M.R. Hestenes and E. Steifel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand, 6(49) (1952), 409-436.
Nocedal J., Theory of Algorithms for Unconstraint Optimization, Acta Numerica, (1992), 199-242.
R. Fletcher, and C. Reeves, Function minimization by conjugate gradients, Comput. J., (7) (1964), 149-154.
Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Comput. Appl. Math., (69) (1991), 129-137.
Y.H. Dai & Y. Yuan, A nonlinear conjugate gradient with a strong global convergence property, SIAM J. Optim., 10(1) (1999), 177–182.
Z. Salleh, G. Alhamzi, I. Masmali and A. Alhawarat, A Modiﬁed Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems, Algorithms, 277(14) (2021)
Zhang, L. A derivative-free conjugate residual method using secant condition for general large-scale nonlinear equations. Numer. Algorithms (83) (2020), 1277–1293.
Zoutendijk G., Nonlinear Programming Computational Methods, Integer and Nonlinear Programming, J. Ababie (Ed), North-Holand. Amsterd, (1970), 37-86.
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