Another modified dprp conjugate gradient method with global convergent properties
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| internalnotes | [1] B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Phys. 9 (1969), 94-112. [2] E. Dolan and J. J. More, Benchmarking optimization software with performance profile, Math. Program. 91 (2002), 201-213. [3] G. Zoutendijk, Nonlinear programming computational methods, Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1970, pp. 37-86. [4] G. Yuan, X. Lu and Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519-530. [5] J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2 (1992), 21-42. [6] M. Rivaie, M. Mamat, J. Leong and M. Ismail, A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comput. 218 (2012), 11323-11332. [7] N. Andrei, Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization, ICI Technical, Report, 13/08, 2008. [8] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [9] Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (1999), 177-182. [10] M. R. Hestenes and E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409-436. [11] R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, Computer Journal 7 (1964), 149-154. [12] R. Fletcher, Practical Method of Optimization, 2nd ed., Unconstrained Optimization, Vol. I, Wiley, New York, 1987. [13] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optim. Theory Appl. 69 (1991), 129-137. [14] M. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. [15] M. Mamat, M. Rivaie, M. Ismail and M. Fauzi, A new conjugate gradient coefficient for unconstrained optimization, Int. J. Contemp. Math. Sci. 5(29) (2010), 1429-1437. [16] I. Jusoh, M. Mamat and M. Rivaie, A new family of conjugate gradient methods for small-scale unconstrained optimization, AIP Conference Proceedings, 1522, 2013, pp. 1360-1365. [17] L. Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215 (2009), 2269-2274. [18] Z. Wei, S. Yao and L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006), 1341-1350. [19] Z. Dai and F. Wen, Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Appl. Math. Comput. 218 (2012), 7421-7430. [20] A. Abashar, M. Mamat, M. Rivaie, M. Ismail and O. Omer, The proof of sufficient descent condition for a new type of conjugate gradient methods, AIP Conference Proceeding 1602, Kuala Lumpur, Malaysia, 2014, pp. 296-303. [21] G. Yuan, X. Lu and Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519-530. |
| originalfilename | 6694-01-FH02-FIK-15-03927.jpg |
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| spelling | 12392 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12392 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal UniSZA Unisza unisza image/jpeg inches 96 96 735 81 81 1416 2015-10-25 09:01:36 1416x735 6694-01-FH02-FIK-15-03927.jpg UniSZA Private Access Another modified dprp conjugate gradient method with global convergent properties Far East Journal of Mathematical Sciences Conjugate gradient (CG) methods play significant role in solving large scale unconstrained optimization problem, due to their low memory requirement and global convergent properties. For many years, different studies and modification have been carried out to improve this method. In this paper, we present a new CG method based on modifying the Abashar et al. [4] method (ADPRP). This new method possesses the global convergent properties and sufficient descent condition under exact line searches. Numerical result based on number of iteration and CPU time shows that the proposed coefficient is efficient and effective when compared with other CG formulas. 98 5 Pushpa Publishing House Pushpa Publishing House 563-577 [1] B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Phys. 9 (1969), 94-112. [2] E. Dolan and J. J. More, Benchmarking optimization software with performance profile, Math. Program. 91 (2002), 201-213. [3] G. Zoutendijk, Nonlinear programming computational methods, Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1970, pp. 37-86. [4] G. Yuan, X. Lu and Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519-530. [5] J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2 (1992), 21-42. [6] M. Rivaie, M. Mamat, J. Leong and M. Ismail, A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comput. 218 (2012), 11323-11332. [7] N. Andrei, Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization, ICI Technical, Report, 13/08, 2008. [8] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [9] Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (1999), 177-182. [10] M. R. Hestenes and E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409-436. [11] R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, Computer Journal 7 (1964), 149-154. [12] R. Fletcher, Practical Method of Optimization, 2nd ed., Unconstrained Optimization, Vol. I, Wiley, New York, 1987. [13] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optim. Theory Appl. 69 (1991), 129-137. [14] M. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. [15] M. Mamat, M. Rivaie, M. Ismail and M. Fauzi, A new conjugate gradient coefficient for unconstrained optimization, Int. J. Contemp. Math. Sci. 5(29) (2010), 1429-1437. [16] I. Jusoh, M. Mamat and M. Rivaie, A new family of conjugate gradient methods for small-scale unconstrained optimization, AIP Conference Proceedings, 1522, 2013, pp. 1360-1365. [17] L. Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215 (2009), 2269-2274. [18] Z. Wei, S. Yao and L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006), 1341-1350. [19] Z. Dai and F. Wen, Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Appl. Math. Comput. 218 (2012), 7421-7430. [20] A. Abashar, M. Mamat, M. Rivaie, M. Ismail and O. Omer, The proof of sufficient descent condition for a new type of conjugate gradient methods, AIP Conference Proceeding 1602, Kuala Lumpur, Malaysia, 2014, pp. 296-303. [21] G. Yuan, X. Lu and Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519-530. |
| spellingShingle | Another modified dprp conjugate gradient method with global convergent properties |
| summary | Conjugate gradient (CG) methods play significant role in solving large scale unconstrained optimization problem, due to their low memory requirement and global convergent properties. For many years, different studies and modification have been carried out to improve this method. In this paper, we present a new CG method based on modifying the Abashar et al. [4] method (ADPRP). This new method possesses the global convergent properties and sufficient descent condition under exact line searches. Numerical result based on number of iteration and CPU time shows that the proposed coefficient is efficient and effective when compared with other CG formulas. |
| title | Another modified dprp conjugate gradient method with global convergent properties |
| title_full | Another modified dprp conjugate gradient method with global convergent properties |
| title_fullStr | Another modified dprp conjugate gradient method with global convergent properties |
| title_full_unstemmed | Another modified dprp conjugate gradient method with global convergent properties |
| title_short | Another modified dprp conjugate gradient method with global convergent properties |
| title_sort | another modified dprp conjugate gradient method with global convergent properties |