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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Journal ArticleDOI
Restoring Solution of Electric Network Equations: An Approach Using the Augmented Lagrangean Algorithm
TL;DR: In this article, the unsolvable power flow is modelled as an constrained optimization problem and solved using an algorithm based on Augmented Lagrangean method that considers the special structure of the proposed problem.
Journal ArticleDOI
Convergence property and modifications of a memory gradient method
TL;DR: Numerical results show that modified memory gradient methods are effective in solving large-scale minimization problems, including the global convergence and rate of convergence.
Efficient simulation of contacts,friction and constraints using a modified spectral projected gradient method
TL;DR: A modified version of the Spectral Proje cted Gradient method that can be used for simulating dynamical systems with complex joints and frictional conta cts and is attractive as a general purpose solver for both linear and non linear problems.
Journal ArticleDOI
Applying Powell's symmetrical technique to conjugate gradient methods
Liu Dongyi,Xu Genqi +1 more
TL;DR: A new conjugate gradient method is proposed by applying Powell’s symmetrical technique to conjugates gradient methods in this paper and the numerical results show that these algorithms are competitive compared with the PRP+ algorithm.
A new efficient variable learning rate for perry’s spectral conjugate gradient training method
TL;DR: A scaled version of the conjugate gradient method suggested by Perry, which employ the spectral steplength of Barzilai and Borwein, was presented and a new acceptability criterion for the learning rate was utilized based on nonmonotone Wolfe conditions.
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.