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On Modified DFP Update for Unconstrained Optimization
American Journal of Applied Mathematics
Volume 5, Issue 1, February 2017, Pages: 19-30
Received: Dec. 25, 2016; Accepted: Jan. 9, 2017; Published: Feb. 6, 2017
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Saad Shakir Mahmood, Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq
Samira Hassan Shnywer, Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq
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In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called update. This update is based on a new Zhang Xu condition we show that update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify method with the standard DFP method on same function is selected.
Quasi-Newton Equation, the DFP Updating Formula, Global Convergence and Super Linearly Convergence
To cite this article
Saad Shakir Mahmood, Samira Hassan Shnywer, On Modified DFP Update for Unconstrained Optimization, American Journal of Applied Mathematics. Vol. 5, No. 1, 2017, pp. 19-30. doi: 10.11648/j.ajam.20170501.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Al-Bayati, A., (1991), A new family of self-scaling variable metric Algorithms for unconstraint optimization, Journal of Educ. and Sci., Iraq, Vol. 12, pp. 25-54.
Dennis J. E., More J., (1974), "A characterization of super linear Convergence and its application to quasi-Newton methods Math and Computation 28 (6) 549-60.
F. Freudenstein and B. Roth,(1962), Numerical solution of system of nonlinear equations, Journal of ACM, Vol. 10, No. 4, pp. 550-556.
H. H. Rosen brock, (1960), An automatic method for finding the greatest least value of a function, Computer Journal, Vol. 3, No. 3, pp. 175-184.
J. E. Dennis, Jr. and Robert B. Schnabel, (1996), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Classics in Applied Mathematics.
Oren, S. S (1973), Self-scaling Variable Metric Algorithms without line search for Unconstrained minimization. Mathematics of computation, 27: 873-885.
Saad S. Mahmood, (2011), α-BFGS update for Unconstrained Opt-imization, Journal of college of Education, No. 1, Almustansiriya University.
Todd M. J., (1984), Quasi-Newton updates in abstract spaces, SIAM Review, 26: 367-377.
W. Sun and Y. Yuan, (2006), "Optimization Theory and Method: Nonlinear Programing", Vol. 1 of Springer optimization and its Applications, Springer, New York, NY, USA.
Yuan, Y., (1990), On a Modified Algorithm for Unconstrained Optimization, Computing Center, Academia Sinica, Beijing, China.
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