Journal ArticleDOI
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
TLDR
Results indicate that the global Barzilai and Borwein method may allow some significant reduction in the number of line searches and also in theNumber of gradient evaluations.Abstract:
The Barzilai and Borwein gradient method for the solution of large scale unconstrained minimization problems is considered. This method requires few storage locations and very inexpensive computations. Furthermore, it does not guarantee descent in the objective function and no line search is required. Recently, the global convergence for the convex quadratic case has been established. However, for the nonquadratic case, the method needs to be incorporated in a globalization scheme. In this work, a nonmonotone line search strategy that guarantees global convergence is combined with the Barzilai and Borwein method. This strategy is based on the nonmonotone line search technique proposed by Grippo, Lampariello, and Lucidi [SIAM J. Numer. Anal., 23 (1986), pp. 707--716]. Numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented. These results indicate that the global Barzilai and Borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations.read more
Citations
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An Algor ithm for Impulsive Noise Removal in Color images
Jianjun Zhang,Xuehua Tang +1 more
TL;DR: Extensive computer simulations indicate that the proposed algorithm provides significant improvement over many of the existing filtering algorithms in suppressing impulsive noise in color images.
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Distributed Machine Learning with Sparse Heterogeneous Data.
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Inexact free derivative quasi-Newton method for large-scale nonlinear system of equations
TL;DR: In this paper , a free derivative quasi-Newton method for solving large-scale nonlinear systems of equation is proposed, where a two-stage linear search direction is introduced and its global convergence theory is developed.
Restoring solution for unsolvable power flow: an approach using the augmented lagrangian algorithm
TL;DR: In this paper, the unsolvable power flow is modelled as a constrained optimization problem and solved using an algorithm based on Aug- mented Lagrangian methods considering the particular structure of the problem, and inner iterations of the pro- posed methodology are solved using Levenberg- Marquardt (LM) algorithm.
References
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Book
Practical Methods of Optimization
TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.
Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Journal ArticleDOI
Two-Point Step Size Gradient Methods
TL;DR: Etude de nouvelles methodes de descente suivant le gradient for the solution approchee du probleme de minimisation sans contrainte. as mentioned in this paper.