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
Characterization of micrometric and superficial residual stresses using high frequency surface acoustic waves generated by interdigital transducers.
Marc Duquennoy,Mohammadi Ouaftouh,Julien Deboucq,Jean-Etienne Lefebvre,Frédéric Jenot,Mohamed Ourak +5 more
TL;DR: The design and implementation of SAW-IDT MEMS sensors enabled quasi-monochromatic Rayleigh-type surface waves to be generated and the dispersion phenomenon to be studied over a wide range of frequencies.
Journal ArticleDOI
Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization
Weijun Zhou,Li Zhang +1 more
TL;DR: A new nonmonotone Armijo type line search is proposed and it is proved that the MBFGS method proposed by Li and Fukushima with this new line search converges globally for nonconvex minimization.
Journal ArticleDOI
Nonlinear least squares and Sobolev gradients
TL;DR: In this article, a trust region subproblems is defined by a Sobolev norm and solved by a preconditioned conjugate gradient method with an effective preconditionaler.
Journal ArticleDOI
Descent direction method with line search for unconstrained optimization in noisy environment
TL;DR: A two-phase descent direction method for unconstrained stochastic optimization problem is proposed, and the almost sure convergence of the proposed method is established, under standard assumption for descent direction and SA methods.
Journal ArticleDOI
Robust Orthogonal Complement Principal Component Analysis
Yiyuan She,Shijie Li,Dapeng Wu +2 more
TL;DR: A novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed, which combines the popular sparsity-enforcing and low-rank regularization techniques to deal with row-wise outliers as well as element-wise outsiers.
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.