TY - JOUR T1 - New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods AU - Abbo, Khalil AU - Hameed, Nehal PY - 2019 DA - January JF - Journal of Multidisciplinary Modeling and Optimization JO - jmmo PB - Ahmet ŞAHİNER WT - DergiPark SN - 2645-923X SP - 91 EP - 99 VL - 1 IS - 2 LA - en AB - In this paper we consider a newhybrid conjugate gradient algorithm, which is convex combination of theLiu-Story algorithm and Dixon algorithm, the descent property and globalconvergence are proved for the new suggested method. Numerical comparisons showthat the present method often behaves better than Liu-Storey and Dixon methods. KW - Conjugate gradient KW - Descente property CR - [1] N. Andrei , New hybrid conjugate gradient algorithms for unconstrained optimization, Enc. Mat. Sci., 2009 2560-2571.[2] N. Andrei, An unconstrained optimization test function collection, Adv. Model. Optim., 10(1) 2008, 147-161.[3] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1), 1993, 123–160 [4] Y. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global con-vergence property, SIAM J. Optimiz., 10(1) 1999, 177-182.[5 L. C. W. Dixon, Nonlinear optimisation: A survey of the state of the art, Hatfield Polytech-nic. Numerical Optimisation Centre (1973). [6] D. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.[7] E. K. Chong and S. H. Zak, An introduction to optimization, John Wiley & Sons 2013. [8] R. Fletcher and C. M. Reeves, Function minimization by Conjugate gradients, comput. J., 7(2) 1964, 149-154.[9] W. Hager and H. Zhang , A survey of nonlinear conjugate gradient methods, Pac. J. Op-tim., 2(1) 2006, 35-58.[10] M. Hestenes and E. Stiefel, Methods of conjugate Gradients For solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952. [11] K. K. Abbo and L. A. Abdulwahid, Generalized Dai-Yuan non-linear conjugate gradi-ent method for unconstrained optimization, Int. J. Sci. Math. Educ., 8(6) 2017, 17993-17999. [12] X. Li and X. Zhao, A hybrid conjugate gradient method for optimization problems, Nat. Sci., 3(1) 2011, 85. [13] Y. Liu and C. Story, Efficient generalized conjugate gradient algorithms, part l : Theory, J. Optimiz. Theory App., 69(1) 1991, 129-137. [14] J. Nocedal and J. Wright, Numerical Optimization, Springer Series in Operations Re-search, Springer Verlag, New York, 2006. [15] E. Polak and G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Rev. Fr. Inform. Rech. O., 3(16) 1969, 35-43.[16] S. S. Djordjević, New hybrid conjugate gradient method as a convex combination of FR and PRP Methods. Filomat, 30(11) 2016, 3083-3100. [17] P. Wolfe, Convergence conditions for ascent methods, SIAM rev., 11(2) 1969, 226-235. UR - https://dergipark.org.tr/tr/pub/jmmo/issue//477127 L1 - https://dergipark.org.tr/tr/download/article-file/631980 ER -