A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization

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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.
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spelling 15242 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=15242 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 13 1.6 Adobe Acrobat 20.6 2024-08-30 11:27:48 6035-01-FH02-FIK-15-03320.pdf UniSZA Private Access A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization Far East Journal of Mathematical Sciences (FJMS) Currently, Zhang [17] takes some modification of the Wei-Yao-Liu nonlinear conjugate gradient method suggested by Wei et al. [18] such that the modified method called NPRP method. Dai and Wen [19] make a simple modification to the NPRP called DPRP method. In this paper, we change denominator of DPRP method such that the modified DPRP method possesses global convergence under exact line search. Numerical results show that the proposed method is efficient for the given test functions when compared with classical formula and DPRP method. 97 1 Pushpa Publishing House Pushpa Publishing House 31-44 [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 A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
summary Currently, Zhang [17] takes some modification of the Wei-Yao-Liu nonlinear conjugate gradient method suggested by Wei et al. [18] such that the modified method called NPRP method. Dai and Wen [19] make a simple modification to the NPRP called DPRP method. In this paper, we change denominator of DPRP method such that the modified DPRP method possesses global convergence under exact line search. Numerical results show that the proposed method is efficient for the given test functions when compared with classical formula and DPRP method.
title A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
title_full A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
title_fullStr A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
title_full_unstemmed A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
title_short A Modified Dprp Conjugate Gradient Method For Unconstrained Optimization
title_sort modified dprp conjugate gradient method for unconstrained optimization