A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization

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internalnotes [1] 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 [2] E. Polak and G. Ribiere, “Note Sur La Convergence de Methodes de Directions Conjuguees,” RevueFrancaised Informatiquet de Recherche Opertionelle, 3(16) (1969), 35–43. [3] M. R. Hestenes and E. L. Stiefel, “Methods of Conjugate Gradients for Solving Linear Systems,” J. Res. Nat. Bur. Standards Sect. 5, 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [4] Y. Liu and C. Storey, “Efficient Generalized Conjugate Gradient Algorithms. I. Theory,” Journal of Optimization Theory and Applications, 69 (1) (1991), 129– 137. http://dx.doi.org/10.1007/bf00940464 [5] Y. H. Dai and Y. Yuan, “A Nonlinear Conjugate Gradient Method with A Strong Global Convergence Property,” SIAM Journal on Optimization, 10 (1) (1999), 177–182. http://dx.doi.org/10.1137/s1052623497318992 [6] M. Rivaie, M. Mamat, W.J. Leong, and I. Mohd. “A New Class of Nonlinear Conjugate Gradient Coefficients with Global Convergence Properties.” Applied Mathematics and Computations. 218 (2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [7] J. C. Gilbert, and J. Nocedal, “Global Convergence Properties of Conjugate Gradient Methods for Optimization,” SIAM J., Optimization. 2 (1) (1992), 21-42. http://dx.doi.org/10.1137/0802003 [8] 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 [9] J. Nocedal and J. Wright, Numerical Optimization, Springer Series In Operations Research, Springer Verlag, New York., USA, (2006). http://dx.doi.org/10.1007/978-0-387-40065-5 [10] J. Nocedal, “Conjugate Gradient Methods and Nonlinear Optimization,” in Linear and Nonlinear Conjugate Gradient-Related Methods (Seattle, WA, 1995), L. Adams and J. L. Nazareth, Eds., 9–23, SIAM, Philadelphia, Pa, USA, 1996. [11] E. Polak, Optimization: Algorithms and Consistent Approximations, vol. 124 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1997. http://dx.doi.org/10.1007/978-1-4612-0663-7 [12] Y. Yuan and W. Sun, “Theory and Methods of Optimization,” Science Press of China, Beijing, China, 1999. [13] N. Andrei, An Unconstrained Optimization Test Functions Collection. Advanced Modelling and Optimization, 10 (1) (2008), 147-161. [14] A. A. Goldstein, On steepest descent, SIAM J. Control. 3 (1965) 147–151. http://dx.doi.org/10.1137/0303013 [15] L. Armijo, Minimization of functions having Lipschitz continuous partial derivatives, Pacific J. Math. 16 (1966) 1–3. http://dx.doi.org/10.2140/pjm.1966.16.1 [16] P. Wolfe, Convergence conditions for ascent method, SIAM Rev. 11 (1969) 226–235. http://dx.doi.org/10.1137/1011036 [17] R. Pytlak, Conjugate gradient algorithm in nonconvex optimization, Springer-Verlag, Berlin, 2009. http://dx.doi.org/10.1007/978-3-540-85634-4 [18] K. E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305–315. http://dx.doi.org/10.1145/355759.355760 [19] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, O. Omer, The Proof of Sufficient Descent Condition for a New Type of Conjugate Gradient Methods, AIP Conf. Proc. 1602 (2014)., 296-303. http://dx.doi.org/10.1063/1.4882502 [20] N. H. M. Yussoff, M. Mamat, M. Rivaie, I. Mohd, A New Conjugate Gradient Methods for Unconstrained Optimization with Sufficient Descent, AIP Conf. Proc. 1602 (2014), 514-519. http://dx.doi.org/10.1063/1.4882534 [21] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, Global Convergence Properties of a New Class of Conjugate Gradient Methods for Unconstrained Optimization, Applied Math. Sci., 8 (67) (2014), 3307-3319. [22] S. Shoid, M. Rivaie, M. Mamat, I. Mohd, Solving Unconstrained Optimization with a New Type of Conjugate Gradient Method, AIP Conf. Proc. 1602 (2014), 574-579. http://dx.doi.org/10.1063/1.4882542 [23] M. Rivaie, A. Abashar, M. Mamat, I. Mohd, The Convergence Properties of a New Type of Conjugate Gradient Methods, Applied Math. Sci., Vol. 8 (1) (2014), 33-44. [24] O. Omer, M. Mamat, A. Abashar, M. Rivaie, The Global Convergence Properties of a Conjugate Gradient Method, AIP Conf. Proc. 1602 (2014), 286- 295. http://dx.doi.org/10.1063/1.4882501 [25] N. Shapiee, M. Rivaie, M. Mamat, I. Mohd, A New Modification of HestenesStiefel with Descent Properties, AIP Conf. Proc. 1602 (2014), 520-526. http://dx.doi.org/10.1063/1.4882535 [26] M. Mamat, M. Rivaie, I. Mohd, M. Fauzi, A New Conjugate Gradient Methods for Unconstrained Optimization, Int. J. Contemp. Math. Sciences, 5 (29) (2010), 1429-1437. [27] M. Hamoda, A. Abashar, M. Mamat, M. Rivaie, A Comparative Study of Two New Conjugate Gradient Methods, AIP Conf. Proc. 1643 (2015), 616-621. http://dx.doi.org/10.1063/1.4907502
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spelling 11934 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11934 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 PPI Trainer 2024-08-26 17:52:15 6235-01-FH02-FIK-15-03339.pdf UniSZA Private Access A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization Applied Mathematical Sciences Conjugate gradient (CG) methods are important in solving unconstrained optimization especially for large-scale unconstrained optimization. In this paper, we proposed a new simple CG coefficient. The global convergence result is established by using exact line search. Numerical results based on number of iterations and CPU time. Numerical result shows that our method is efficient when compared to the other CG coefficients for a given standard test problems. 9 63 HIKARI Ltd. HIKARI Ltd. 3119-3130 [1] 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 [2] E. Polak and G. Ribiere, “Note Sur La Convergence de Methodes de Directions Conjuguees,” RevueFrancaised Informatiquet de Recherche Opertionelle, 3(16) (1969), 35–43. [3] M. R. Hestenes and E. L. Stiefel, “Methods of Conjugate Gradients for Solving Linear Systems,” J. Res. Nat. Bur. Standards Sect. 5, 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [4] Y. Liu and C. Storey, “Efficient Generalized Conjugate Gradient Algorithms. I. Theory,” Journal of Optimization Theory and Applications, 69 (1) (1991), 129– 137. http://dx.doi.org/10.1007/bf00940464 [5] Y. H. Dai and Y. Yuan, “A Nonlinear Conjugate Gradient Method with A Strong Global Convergence Property,” SIAM Journal on Optimization, 10 (1) (1999), 177–182. http://dx.doi.org/10.1137/s1052623497318992 [6] M. Rivaie, M. Mamat, W.J. Leong, and I. Mohd. “A New Class of Nonlinear Conjugate Gradient Coefficients with Global Convergence Properties.” Applied Mathematics and Computations. 218 (2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [7] J. C. Gilbert, and J. Nocedal, “Global Convergence Properties of Conjugate Gradient Methods for Optimization,” SIAM J., Optimization. 2 (1) (1992), 21-42. http://dx.doi.org/10.1137/0802003 [8] 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 [9] J. Nocedal and J. Wright, Numerical Optimization, Springer Series In Operations Research, Springer Verlag, New York., USA, (2006). http://dx.doi.org/10.1007/978-0-387-40065-5 [10] J. Nocedal, “Conjugate Gradient Methods and Nonlinear Optimization,” in Linear and Nonlinear Conjugate Gradient-Related Methods (Seattle, WA, 1995), L. Adams and J. L. Nazareth, Eds., 9–23, SIAM, Philadelphia, Pa, USA, 1996. [11] E. Polak, Optimization: Algorithms and Consistent Approximations, vol. 124 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1997. http://dx.doi.org/10.1007/978-1-4612-0663-7 [12] Y. Yuan and W. Sun, “Theory and Methods of Optimization,” Science Press of China, Beijing, China, 1999. [13] N. Andrei, An Unconstrained Optimization Test Functions Collection. Advanced Modelling and Optimization, 10 (1) (2008), 147-161. [14] A. A. Goldstein, On steepest descent, SIAM J. Control. 3 (1965) 147–151. http://dx.doi.org/10.1137/0303013 [15] L. Armijo, Minimization of functions having Lipschitz continuous partial derivatives, Pacific J. Math. 16 (1966) 1–3. http://dx.doi.org/10.2140/pjm.1966.16.1 [16] P. Wolfe, Convergence conditions for ascent method, SIAM Rev. 11 (1969) 226–235. http://dx.doi.org/10.1137/1011036 [17] R. Pytlak, Conjugate gradient algorithm in nonconvex optimization, Springer-Verlag, Berlin, 2009. http://dx.doi.org/10.1007/978-3-540-85634-4 [18] K. E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305–315. http://dx.doi.org/10.1145/355759.355760 [19] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, O. Omer, The Proof of Sufficient Descent Condition for a New Type of Conjugate Gradient Methods, AIP Conf. Proc. 1602 (2014)., 296-303. http://dx.doi.org/10.1063/1.4882502 [20] N. H. M. Yussoff, M. Mamat, M. Rivaie, I. Mohd, A New Conjugate Gradient Methods for Unconstrained Optimization with Sufficient Descent, AIP Conf. Proc. 1602 (2014), 514-519. http://dx.doi.org/10.1063/1.4882534 [21] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, Global Convergence Properties of a New Class of Conjugate Gradient Methods for Unconstrained Optimization, Applied Math. Sci., 8 (67) (2014), 3307-3319. [22] S. Shoid, M. Rivaie, M. Mamat, I. Mohd, Solving Unconstrained Optimization with a New Type of Conjugate Gradient Method, AIP Conf. Proc. 1602 (2014), 574-579. http://dx.doi.org/10.1063/1.4882542 [23] M. Rivaie, A. Abashar, M. Mamat, I. Mohd, The Convergence Properties of a New Type of Conjugate Gradient Methods, Applied Math. Sci., Vol. 8 (1) (2014), 33-44. [24] O. Omer, M. Mamat, A. Abashar, M. Rivaie, The Global Convergence Properties of a Conjugate Gradient Method, AIP Conf. Proc. 1602 (2014), 286- 295. http://dx.doi.org/10.1063/1.4882501 [25] N. Shapiee, M. Rivaie, M. Mamat, I. Mohd, A New Modification of HestenesStiefel with Descent Properties, AIP Conf. Proc. 1602 (2014), 520-526. http://dx.doi.org/10.1063/1.4882535 [26] M. Mamat, M. Rivaie, I. Mohd, M. Fauzi, A New Conjugate Gradient Methods for Unconstrained Optimization, Int. J. Contemp. Math. Sciences, 5 (29) (2010), 1429-1437. [27] M. Hamoda, A. Abashar, M. Mamat, M. Rivaie, A Comparative Study of Two New Conjugate Gradient Methods, AIP Conf. Proc. 1643 (2015), 616-621. http://dx.doi.org/10.1063/1.4907502
spellingShingle A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
summary Conjugate gradient (CG) methods are important in solving unconstrained optimization especially for large-scale unconstrained optimization. In this paper, we proposed a new simple CG coefficient. The global convergence result is established by using exact line search. Numerical results based on number of iterations and CPU time. Numerical result shows that our method is efficient when compared to the other CG coefficients for a given standard test problems.
title A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
title_full A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
title_fullStr A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
title_full_unstemmed A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
title_short A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization
title_sort new simple conjugate gradient coefficient for unconstrained optimization