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
Minimization Algorithms Based on Supervisor and Searcher Cooperation
Wenbin Liu,Yu-Hong Dai +1 more
TL;DR: This work proposes a class of algorithms within this framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation, and examines a gradient algorithm in the class.
Journal ArticleDOI
Nonmonotone line search methods with variable sample size
TL;DR: Nonmonotonicity of the line search combines well with the variable sample size scheme as it allows more freedom in choosing the search direction and the step size while the sample size is not the maximal one and increases the chances of finding a global solution.
Journal ArticleDOI
A Barzilai-Borwein conjugate gradient method
Yu-Hong Dai,CaiXia Kou +1 more
TL;DR: If choosing the parameter in the method by combining the Barzilai-Borwein idea, the initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches and might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.
Journal ArticleDOI
Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method
TL;DR: In this article, a spectral projected gradient method (SPGM) is used to minimize the difference between measured and computed transmittance spectra, which is a powerful tool to solve efficiently the problem of obtaining the optical constants of thin films from spectroscopic measurements.
Journal ArticleDOI
Convergence of descent method without line search
Zhen-Jun Shi,Jie Shen +1 more
TL;DR: A new descent method without line search for unconstrained optimization problems is proposed, and theoretically the global convergence of the new algorithm under mild conditions is analyzed.
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.