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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Spectral Projected Gradient Methods
Ernesto G. Birgin,Marcos Raydan +1 more
TL;DR: In this paper, it was shown that the structure of the iteration (1)-(2) is very attractive, especially when one deals with large-scale (many variables) problems.
Journal ArticleDOI
A new nonmonotone spectral residual method for nonsmooth nonlinear equations
Shuai Huang,Zhong Wan +1 more
TL;DR: A new derivative-free algorithm, called a nonmonotone spectral residual algorithm (NSRA), is developed to solve systems of large-scale nonlinear equations, where the steplength is obtained by minimizing the residue of an approximate secant equation.
Journal ArticleDOI
A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations
TL;DR: Preliminary numerical results show that the proposed Hager–Zhang Conjugate Gradient methods are promising and more efficient compared to the methods presented by Mushtak and Keyvan (2018) and Sun et al. (2017).
Journal ArticleDOI
A new spectral conjugate gradient method for large-scale unconstrained optimization
TL;DR: A new approach for generating spectral parameters is presented, where a new double-truncating technique, which can ensure both the sufficient descentproperty of the search directions and the bounded property of the sequence of spectral parameters, is introduced.
Journal ArticleDOI
A Two-Step Spectral Gradient Projection Method for System of Nonlinear Monotone Equations and Image Deblurring Problems
TL;DR: A new line search technique for generating the separating hyperplane projection step of Solodov and Svaiter (1998) that generalizes the one used in most of the existing literature is presented and the convergence result of the algorithm is established.
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.