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
More filters
Journal ArticleDOI
Total variation method based on modified Barzilai–Borwein algorithm to noise reduction in MRI images
Journal Article
Nonlinear Regularization for Bi-level Image Restoration
Zhang Jian-jun,Wang Qin +1 more
TL;DR: In this paper, a nonlinear regularization method for bi-level image restoration by explicitly using the knowledge of the bilevel image was proposed, which leads to a non-linear optimiza- tion problem, solved with the global Barzilai and Borwein gradient method.
Dissertation
Sobre minimização de quadraticas em caixas
TL;DR: The GENCAN algorithm as discussed by the authors minimizes funcoes em caixas by pre-condicionar the gradient conjugados. But, as shown in Fig. 1, a precondicionador used in this software mostrou-se computacionalmente caro.
A New Hessian Approximation for Non-Convex Unconstrained Minimization Methods
TL;DR: This method selects the step-length according to a modified backtracking procedure, along the negative gradient, using a new scalar approximation of the Hessian of the minimization function based on the function values and its gradients in two successive points along the iterations.
Journal ArticleDOI
Spectral Gradient Algorithm Based on the Generalized Fiser-Burmeister Function for Sparse Solutions of LCPS
TL;DR: An lp(0 < p < 1) regularized minimization model is proposed for relaxation and the equivalent unconstrained minimization reformation of the NCP-function is established.
References
More filters
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.