A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization
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| internalnotes | [1] N. Andrei, "An unconstrained optimization test functions collection," Advanced Modeling and Optimization, 10 (2008), 147-161. [2] Y.-H. Dai and Y. Yuan, "A nonlinear conjugate gradient method with a strong global convergence property," SIAM Journal on Optimization, 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [3] Y. H. Dai, "Convergence of nonlinear conjugate gradient methods," Journal of Computational Mathematics, 19 (2001), 539-548. [4] Y. H. Dai and Y. Yuan, "Further studies on the Polak-Ribiere-Polyak method," Research report ICM-95-040, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences1995. [5] E. D. Dolan and J. J. Mor, "Benchmarking optimization software with performance profiles," Mathematical Programming, 91 (2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [6] R. Fletcher, Practical Method of Optimization, 2 ed. I. New York, 1987. http://dx.doi.org/10.1002/9781118723203 [7] R. Fletcher and C. M. Reeves, "Function minimization by conjugate gradients," The computer journal, 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [8] J. C. Gilbert and J. Nocedal, "Global convergence properties of conjugate gradient methods for optimization," SIAM J. Optim., 2 (1992), 21-42. http://dx.doi.org/10.1137/0802003 [9] L. Grippo and S. Lucidi, "A globally convergent version of the Polak-Ribière conjugate gradient method," Math. Program., 78 (1997), 375–391. http://dx.doi.org/10.1007/bf02614362 [10] H. Hai, Y. Shengwei, and L. Suihua, "A new conjugate gradient method combined HS and DY formulas," M. a. I. Science, Ed., ed: Guangxi University, 2006. [11] M. R. Hestenes and E. Stiefel, "Method of conjugate gradient for solving linear systems," J. Res. Nat. Bur. Stand., 49 (1952), 409–436. http://dx.doi.org/10.6028/jres.049.044 [12] K. E. Hillstrom, "A simulation test approach to the evaluation of nonlinear optimization algorithms," ACM Transactions on Mathematical Software 3 (1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [13] W. J. Z. L. Zhang, D.H. Li, "Global convergence of a modified Fletcher–Revves conjugate gradient method with Armijo-type line search," Numer. Math. , 104 (2006), 561–572. http://dx.doi.org/10.1007/s00211-006-0028-z [14] Y. Liu and C. Storey, "Efficient generalized conjugate gradient algorithms, Part 1: Theory," Journal of Optimization Theory and Applications, 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [15] E. Polak and G. Ribiere, "Note Sur la convergence de directions conjuge`es," Rev. Francaise Informat Recherche Operationelle, 3E (1969), 35–43. [16] B. T. Polyak, "The conjugate gradient method in extreme problems," USSR Computational Mathematics and Mathematical Physics, 9 (1969), 94–112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [17] M. J. Powell, "Nonconvex minimization calculations and the conjugate gradient method," in Numerical analysis, ed: Springer, 122-141, 1984. http://dx.doi.org/10.1007/bfb0099521 [18] M. J. D. Powell, "Restart procedures for the conjugate gradient method," Mathematical Programming 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [19] 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. http://dx.doi.org/10.1016/j.amc.2012.05.030 [20] D. Touati-Ahmed and C. Storey, "Globally convergent hybrid conjugate gradient methods," J. Optim. Theory Appl., 64 (1990), 379–397. [21] Z. X. Wei, S. W. Yao, and L. Y. Liu, "The convergence properties of some new conjugate gradient methods," Applied Mathematics and Computation, 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [22] G. Zoutendijk, "Nonlinear programming, computational methods," in Integer and nonlinear programming, ed North-Holland, Amsterdam, 37-86, 1970. |
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| spelling | 11931 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11931 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal application/pdf Adobe Acrobat Pro DC 20 Paper Capture Plug-in with ClearScan 11 1.6 HP Hp hp 2024-08-26 17:47:48 6232-01-FH02-FIK-15-03336.pdf UniSZA Private Access A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization Applied Mathematical Sciences In this paper, we suggest a new nonlinear conjugate gradient method for solving large scale unconstrained optimization problems. We prove that the new conjugate gradient coefficient β k with exact line search is globally convergent. Preliminary numerical results with a set of 116 unconstrained optimization problems show that β k is very promising and efficient when compared to the other conjugate gradient coefficients Fletcher - Reeves (FR) and Polak -Ribiere – Polyak (PRP). 9 37 HIKARI Ltd. HIKARI Ltd. 1813-1822 [1] N. Andrei, "An unconstrained optimization test functions collection," Advanced Modeling and Optimization, 10 (2008), 147-161. [2] Y.-H. Dai and Y. Yuan, "A nonlinear conjugate gradient method with a strong global convergence property," SIAM Journal on Optimization, 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [3] Y. H. Dai, "Convergence of nonlinear conjugate gradient methods," Journal of Computational Mathematics, 19 (2001), 539-548. [4] Y. H. Dai and Y. Yuan, "Further studies on the Polak-Ribiere-Polyak method," Research report ICM-95-040, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences1995. [5] E. D. Dolan and J. J. Mor, "Benchmarking optimization software with performance profiles," Mathematical Programming, 91 (2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [6] R. Fletcher, Practical Method of Optimization, 2 ed. I. New York, 1987. http://dx.doi.org/10.1002/9781118723203 [7] R. Fletcher and C. M. Reeves, "Function minimization by conjugate gradients," The computer journal, 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [8] J. C. Gilbert and J. Nocedal, "Global convergence properties of conjugate gradient methods for optimization," SIAM J. Optim., 2 (1992), 21-42. http://dx.doi.org/10.1137/0802003 [9] L. Grippo and S. Lucidi, "A globally convergent version of the Polak-Ribière conjugate gradient method," Math. Program., 78 (1997), 375–391. http://dx.doi.org/10.1007/bf02614362 [10] H. Hai, Y. Shengwei, and L. Suihua, "A new conjugate gradient method combined HS and DY formulas," M. a. I. Science, Ed., ed: Guangxi University, 2006. [11] M. R. Hestenes and E. Stiefel, "Method of conjugate gradient for solving linear systems," J. Res. Nat. Bur. Stand., 49 (1952), 409–436. http://dx.doi.org/10.6028/jres.049.044 [12] K. E. Hillstrom, "A simulation test approach to the evaluation of nonlinear optimization algorithms," ACM Transactions on Mathematical Software 3 (1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [13] W. J. Z. L. Zhang, D.H. Li, "Global convergence of a modified Fletcher–Revves conjugate gradient method with Armijo-type line search," Numer. Math. , 104 (2006), 561–572. http://dx.doi.org/10.1007/s00211-006-0028-z [14] Y. Liu and C. Storey, "Efficient generalized conjugate gradient algorithms, Part 1: Theory," Journal of Optimization Theory and Applications, 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [15] E. Polak and G. Ribiere, "Note Sur la convergence de directions conjuge`es," Rev. Francaise Informat Recherche Operationelle, 3E (1969), 35–43. [16] B. T. Polyak, "The conjugate gradient method in extreme problems," USSR Computational Mathematics and Mathematical Physics, 9 (1969), 94–112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [17] M. J. Powell, "Nonconvex minimization calculations and the conjugate gradient method," in Numerical analysis, ed: Springer, 122-141, 1984. http://dx.doi.org/10.1007/bfb0099521 [18] M. J. D. Powell, "Restart procedures for the conjugate gradient method," Mathematical Programming 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [19] 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. http://dx.doi.org/10.1016/j.amc.2012.05.030 [20] D. Touati-Ahmed and C. Storey, "Globally convergent hybrid conjugate gradient methods," J. Optim. Theory Appl., 64 (1990), 379–397. [21] Z. X. Wei, S. W. Yao, and L. Y. Liu, "The convergence properties of some new conjugate gradient methods," Applied Mathematics and Computation, 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [22] G. Zoutendijk, "Nonlinear programming, computational methods," in Integer and nonlinear programming, ed North-Holland, Amsterdam, 37-86, 1970. |
| spellingShingle | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| summary | In this paper, we suggest a new nonlinear conjugate gradient method for solving large scale unconstrained optimization problems. We prove that the new conjugate gradient coefficient β k with exact line search is globally convergent. Preliminary numerical results with a set of 116 unconstrained optimization problems show that β k is very promising and efficient when compared to the other conjugate gradient coefficients Fletcher - Reeves (FR) and Polak -Ribiere – Polyak (PRP). |
| title | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| title_full | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| title_fullStr | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| title_full_unstemmed | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| title_short | A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization |
| title_sort | new nonlinear conjugate gradient coefficient for unconstrained optimization |