Coefficients of modified broyden method and its global convergence

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internalnotes [1] L. Armijo, Minimization of functions having Lipschitz continuous partial derivatives, Pacific J. Math. 16 (1966), 1-3. [2] R. H. Byrd and F. Nocedal, A tool for the analysis of quasi-Newton methods with application to unconstrained minimization, SIAM J. Numer. Anal. 26 (1989), 727-739. [3] A. Goldstein, On steepest descent, Journal of the Society for Industrial and Applied Mathematics Series A Control 3 (1965), 147-151. [4] M. A. H. Ibrahim, M. Mamat and W. J. Leong, The hybrid BFGS-CG method in solving unconstrained optimization problems, Abstr. Appl. Anal. 2014 (2014), 1-6. [5] M. A. H. Ibrahim, M. Mamat, L. W. June and A. Z. M. Sofi, The CG-BFGS method for unconstrained optimization problems, AIP Conf. Proc. 1605 (2014), 167-172. [6] M. Mamat, I. Mohd, L. W. June and Y. Dasril, Hybrid Broyden method for unconstrained optimization, International Journal of Numerical Methods and Applications 1 (2009), 121-130. [7] J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006. [8] Z. -J. Shi, Convergence of quasi-Newton method with new inexact line search, J. Math. Anal. Appl. 315 (2006), 120-131. [9] P. Wolfe, Convergence conditions for ASCENT methods, SIAM Rev. 11 (1969), 226-235. [10] P. Wolfe, Convergence conditions for ASCENT methods. II: Some corrections, SIAM Rev. 13 (1971), 185-188. [11] D. C. Xu, Global convergence of the Broyden’s class of quasi-Newton methods with nonmonotone linesearch, Acta Math. Appl. Sin. 19 (2003), 19-24.
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spelling 13257 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=13257 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 norman 01 01 1422 764 1422x764 2016-10-09 08:17:47 7567-01-FH02-FIK-16-06686.jpg UniSZA Private Access Coefficients of modified broyden method and its global convergence Far East Journal of Mathematical Sciences In this article, a new search direction for the Broyden family method is proposed for solving unconstrained optimization problems. The new search direction is developed by using the search direction of conjugate gradient method approach. This method is popular as M-Broyden method. The suggested method has an attractive property that its search direction is sufficiently descent in every iteration. Under mild conditions, we prove that the proposed method has global convergence. 100 5 Pushpa Publishing House Pushpa Publishing House 795-803 [1] L. Armijo, Minimization of functions having Lipschitz continuous partial derivatives, Pacific J. Math. 16 (1966), 1-3. [2] R. H. Byrd and F. Nocedal, A tool for the analysis of quasi-Newton methods with application to unconstrained minimization, SIAM J. Numer. Anal. 26 (1989), 727-739. [3] A. Goldstein, On steepest descent, Journal of the Society for Industrial and Applied Mathematics Series A Control 3 (1965), 147-151. [4] M. A. H. Ibrahim, M. Mamat and W. J. Leong, The hybrid BFGS-CG method in solving unconstrained optimization problems, Abstr. Appl. Anal. 2014 (2014), 1-6. [5] M. A. H. Ibrahim, M. Mamat, L. W. June and A. Z. M. Sofi, The CG-BFGS method for unconstrained optimization problems, AIP Conf. Proc. 1605 (2014), 167-172. [6] M. Mamat, I. Mohd, L. W. June and Y. Dasril, Hybrid Broyden method for unconstrained optimization, International Journal of Numerical Methods and Applications 1 (2009), 121-130. [7] J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006. [8] Z. -J. Shi, Convergence of quasi-Newton method with new inexact line search, J. Math. Anal. Appl. 315 (2006), 120-131. [9] P. Wolfe, Convergence conditions for ASCENT methods, SIAM Rev. 11 (1969), 226-235. [10] P. Wolfe, Convergence conditions for ASCENT methods. II: Some corrections, SIAM Rev. 13 (1971), 185-188. [11] D. C. Xu, Global convergence of the Broyden’s class of quasi-Newton methods with nonmonotone linesearch, Acta Math. Appl. Sin. 19 (2003), 19-24.
spellingShingle Coefficients of modified broyden method and its global convergence
summary In this article, a new search direction for the Broyden family method is proposed for solving unconstrained optimization problems. The new search direction is developed by using the search direction of conjugate gradient method approach. This method is popular as M-Broyden method. The suggested method has an attractive property that its search direction is sufficiently descent in every iteration. Under mild conditions, we prove that the proposed method has global convergence.
title Coefficients of modified broyden method and its global convergence
title_full Coefficients of modified broyden method and its global convergence
title_fullStr Coefficients of modified broyden method and its global convergence
title_full_unstemmed Coefficients of modified broyden method and its global convergence
title_short Coefficients of modified broyden method and its global convergence
title_sort coefficients of modified broyden method and its global convergence