A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization
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| internalnotes | [1] R. Fletcher and C. Reeves, “Function minimization by conjugate gradients,” Comput. J., 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [2] E. Polak, and G. Ribiere, “Note for Convergence Direction Conjugate”, Revue Françoise Informant, ResercheOpertionelle, 16 (1969), 35-43. [3] M. R. Hestenes and E. Steifel, “Method of conjugate gradient for solving linear equations,” J. Res. Nat. Bur. Stand., 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [4] Y. Liu and C. Storey, “Efficient generalized conjugate gradient algorithms part 1: Theory,” J. Comput. Appl. Math., 69 (1992), 129-137. http://dx.doi.org/10.1007/bf00940464 [5] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [6] Y. Dai and Y. Yuan, “A nonlinear conjugate gradient with a strong global convergence properties,” SIAM J. Optim., 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [7] M. Rivaie, M. Mamat, L. W. June and M. Ismail, “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 [8] G. Zoutendijk, “Nonlinear programming computational methods,” In:Abadie J.(Ed.) Integer and nonlinear programming, 1970, 37-86. [9] M. Al-Baali, “Descent property and global convergence of Fletcher-Reeves method with inexact line search,” IMA. J. Numer. Anal., 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [10] P. Wolfe, “Convergence conditions for ascent method,” SIAM Rev., 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [11] A. A. Goldstein, “On steepest descent”, SIAM J. Control, 3 (1965), 147-151. http://dx.doi.org/10.1137/0303013 [12] L. Armijo, “Minimization of functions having Lipsschitz continuous first partial derivatives, Pac. J. Math., 6 (1966), 1-3. http://dx.doi.org/10.2140/pjm.1966.16.1 [13] M. J. D. Powell, “Restart procedures for the conjugate gradient method,” Mathematical Programming, 12 (1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [14] E. G. Birgin and J. M. Martinez, “A spectral conjugate gradient method for unconstrained optimization,” J. Appl. Maths. Optim, 43 (2001), 117-128. http://dx.doi.org/10.1007/s00245-001-0003-0 [15] N. Andrei, Numerical comparison of conjugate gradient algorithms for unconstrained optimization”, ICI Technical, Report, 10/10(2007). [16] G. Yuan, X. Lu, and Z. Wei, “A Conjugate Gradient Method with Descent Direction for Unconstrained Optimization”. Journal of Computational and Applied Mathematics, 233 (2009), 519-530. http://dx.doi.org/10.1016/j.cam.2009.08.001 [17] N. Andrei, “40 conjugate gradient algorithms for unconstrained optimization”, Bull. Malay. Math. Sci. Soc. 34 (2011), 319-330. [18] H. Iiduka and Y. Narushima, “Conjugate Gradient Method Using Value of Objective Function for Unconstrained Optimization”, OptimLett, 6 (2012), 941-955. http://dx.doi.org/10.1007/s11590-011-0324-0 [19] Y. H. Dai, J.Y. Han, G. H. Liu, D. F. Sun, X. Yin and Y. Yuan, “Converge nce properties of nonlinear conjugate gradient method,” SIAM J. Optim.,10 (2000), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [20] N. Andrei, “An unconstrained optimization test functions collection,” Advanced Modelling and Optimization, 10(1) (2008), 147-161. [21] M. Molga and C. Smutnicki, C. 2005. Test Functions for optimization needs. www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf [22] K. E. Hilstrom, “A simulation test approach to the evaluation of nonlinear optimization algorithms,” A.C.M. Trans. Maths. Softw.3, 4 (1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [23] N. H. M. Yussoff, M. Mamat, M. Rivaie and I. Mohd, “A New Conjugate Gradient Method for Unconstrained Optimization with Sufficient Descent”, AIP Conference Proceedings 1602 (2014), 514-519. http://dx.doi.org/10.1063/1.4882534 [24] Z. Z. Abidin, M. Mamat, M. Rivaie and I. Mohd, “A New Steepest Descent Method”, AIP Conference Proceedings 1602 (2014), 273-278. http://dx.doi.org/10.1063/1.4882499 [25] N. Shapiee, M. Mamat, M. Rivaie and I. Mohd, “A new modification of Hestenes-Stiefel method with descent properties”, AIP Conference Proceedings 1602 (2014), 520-526. http://dx.doi.org/10.1063/1.4882535 [26] S. Shoid, M. Mamat, M. Rivaie and I. Mohd, “Solving unconstrained optimization with a new type of conjugate gradient method”, AIP Conference Proceedings 1602 (2014), 574-580. http://dx.doi.org/10.1063/1.4882542 [27] A. Abashar, M. Mamat, M. Rivaie, I. Mohd and O. Omer, “The proof of sufficient descent condition for a new type of conjugate gradient methods”, AIP Conference Proceedings 1602 (2014), 296-303. http://dx.doi.org/10.1063/1.4882502 [28] O. Omer, M. Mamat, A. Abashar, and M. Rivaie, “The global convergence properties of a conjugate gradient method”, AIP Conference Proceedings 1602 (2014), 286-295. http://dx.doi.org/10.1063/1.4882501 |
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| spelling | 12122 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12122 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal UniSZA Unisza unisza image/jpeg inches 96 96 1418 771 18 18 2015-07-01 12:06:48 1418x771 6422-01-FH02-FIK-15-03430.jpg UniSZA Private Access A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization Applied Mathematical Sciences One of popular methods in solving unconstrained optimization method is conjugate gradient methods (CG). This paper presents a new CG method based on combination of two classical CG methods. Global convergence properties play the important part in CG methods. Numerical result show that this new CG method is quite effective when measured based on number of iteration and CPU times. 9 61 HIKARI Ltd. HIKARI Ltd. 3131-3142 [1] R. Fletcher and C. Reeves, “Function minimization by conjugate gradients,” Comput. J., 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [2] E. Polak, and G. Ribiere, “Note for Convergence Direction Conjugate”, Revue Françoise Informant, ResercheOpertionelle, 16 (1969), 35-43. [3] M. R. Hestenes and E. Steifel, “Method of conjugate gradient for solving linear equations,” J. Res. Nat. Bur. Stand., 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [4] Y. Liu and C. Storey, “Efficient generalized conjugate gradient algorithms part 1: Theory,” J. Comput. Appl. Math., 69 (1992), 129-137. http://dx.doi.org/10.1007/bf00940464 [5] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [6] Y. Dai and Y. Yuan, “A nonlinear conjugate gradient with a strong global convergence properties,” SIAM J. Optim., 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [7] M. Rivaie, M. Mamat, L. W. June and M. Ismail, “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 [8] G. Zoutendijk, “Nonlinear programming computational methods,” In:Abadie J.(Ed.) Integer and nonlinear programming, 1970, 37-86. [9] M. Al-Baali, “Descent property and global convergence of Fletcher-Reeves method with inexact line search,” IMA. J. Numer. Anal., 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [10] P. Wolfe, “Convergence conditions for ascent method,” SIAM Rev., 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [11] A. A. Goldstein, “On steepest descent”, SIAM J. Control, 3 (1965), 147-151. http://dx.doi.org/10.1137/0303013 [12] L. Armijo, “Minimization of functions having Lipsschitz continuous first partial derivatives, Pac. J. Math., 6 (1966), 1-3. http://dx.doi.org/10.2140/pjm.1966.16.1 [13] M. J. D. Powell, “Restart procedures for the conjugate gradient method,” Mathematical Programming, 12 (1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [14] E. G. Birgin and J. M. Martinez, “A spectral conjugate gradient method for unconstrained optimization,” J. Appl. Maths. Optim, 43 (2001), 117-128. http://dx.doi.org/10.1007/s00245-001-0003-0 [15] N. Andrei, Numerical comparison of conjugate gradient algorithms for unconstrained optimization”, ICI Technical, Report, 10/10(2007). [16] G. Yuan, X. Lu, and Z. Wei, “A Conjugate Gradient Method with Descent Direction for Unconstrained Optimization”. Journal of Computational and Applied Mathematics, 233 (2009), 519-530. http://dx.doi.org/10.1016/j.cam.2009.08.001 [17] N. Andrei, “40 conjugate gradient algorithms for unconstrained optimization”, Bull. Malay. Math. Sci. Soc. 34 (2011), 319-330. [18] H. Iiduka and Y. Narushima, “Conjugate Gradient Method Using Value of Objective Function for Unconstrained Optimization”, OptimLett, 6 (2012), 941-955. http://dx.doi.org/10.1007/s11590-011-0324-0 [19] Y. H. Dai, J.Y. Han, G. H. Liu, D. F. Sun, X. Yin and Y. Yuan, “Converge nce properties of nonlinear conjugate gradient method,” SIAM J. Optim.,10 (2000), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [20] N. Andrei, “An unconstrained optimization test functions collection,” Advanced Modelling and Optimization, 10(1) (2008), 147-161. [21] M. Molga and C. Smutnicki, C. 2005. Test Functions for optimization needs. www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf [22] K. E. Hilstrom, “A simulation test approach to the evaluation of nonlinear optimization algorithms,” A.C.M. Trans. Maths. Softw.3, 4 (1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [23] N. H. M. Yussoff, M. Mamat, M. Rivaie and I. Mohd, “A New Conjugate Gradient Method for Unconstrained Optimization with Sufficient Descent”, AIP Conference Proceedings 1602 (2014), 514-519. http://dx.doi.org/10.1063/1.4882534 [24] Z. Z. Abidin, M. Mamat, M. Rivaie and I. Mohd, “A New Steepest Descent Method”, AIP Conference Proceedings 1602 (2014), 273-278. http://dx.doi.org/10.1063/1.4882499 [25] N. Shapiee, M. Mamat, M. Rivaie and I. Mohd, “A new modification of Hestenes-Stiefel method with descent properties”, AIP Conference Proceedings 1602 (2014), 520-526. http://dx.doi.org/10.1063/1.4882535 [26] S. Shoid, M. Mamat, M. Rivaie and I. Mohd, “Solving unconstrained optimization with a new type of conjugate gradient method”, AIP Conference Proceedings 1602 (2014), 574-580. http://dx.doi.org/10.1063/1.4882542 [27] A. Abashar, M. Mamat, M. Rivaie, I. Mohd and O. Omer, “The proof of sufficient descent condition for a new type of conjugate gradient methods”, AIP Conference Proceedings 1602 (2014), 296-303. http://dx.doi.org/10.1063/1.4882502 [28] O. Omer, M. Mamat, A. Abashar, and M. Rivaie, “The global convergence properties of a conjugate gradient method”, AIP Conference Proceedings 1602 (2014), 286-295. http://dx.doi.org/10.1063/1.4882501 |
| spellingShingle | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| summary | One of popular methods in solving unconstrained optimization method is conjugate gradient methods (CG). This paper presents a new CG method based on combination of two classical CG methods. Global convergence properties play the important part in CG methods. Numerical result show that this new CG method is quite effective when measured based on number of iteration and CPU times. |
| title | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| title_full | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| title_fullStr | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| title_full_unstemmed | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| title_short | A combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |
| title_sort | combination of polak-ribiere and hestenes-steifel coefficient in conjugate gradient method for unconstrained optimization |