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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Proceedings ArticleDOI
On the Non-monotone Armijo-type Line Search Algorithm
TL;DR: The numerical results will show that some line search methods with the novel nonmonotone line search are available and efficient in practical computation.
Journal ArticleDOI
Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
TL;DR: This paper globalizes Schubert’s method by using a nonmonotone line search and shows that the proposed algorithm converges globally and superlinearly.
Training Neural Networks using Two-Point Stepsize Gradient Methods
TL;DR: This work develops a sophisticated back-propagation method that automatically adapt the stepsize utilizing information from two points and derives a two-point stepsize by approximating the new secant equation of Zhang et al.
Journal ArticleDOI
A Modified Descent Spectral Conjugate Gradient Method for Unconstrained Optimization
TL;DR: In this paper, a modified secant equation was proposed to approximate the second-order curvature information of the objective function and the sufficient descent condition was proved for uniformly convex functions and general functions.
Journal ArticleDOI
On the complexity of solving feasibility problems with regularized models
TL;DR: The complexity of solving feasibility problems is considered in this work and it is assumed that the constraints that define the problem can be divided into expensive and cheap constraints.
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.