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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Dissertation
Optimal Design of Feeding System in Steel Castings
TL;DR: In this paper, the optimal design of feeding system in steel sand-mold castings is considered, where the authors formulated the problem as a point-wise constrained topology optimization problem.
Journal ArticleDOI
On the worst case performance of the steepest descent algorithm for quadratic functions
TL;DR: It is shown how to construct a sequence of step lengths with which the algorithm stops in O(Clog(1/ε) iterations, with a bound almost exactly equal to that of the Conjugate Gradient method.
Journal ArticleDOI
Simultaneous Reconstruction of Conductivity, Boundary Shape, and Contact Impedances in Electrical Impedance Tomography
TL;DR: The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body.
Journal ArticleDOI
Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization
TL;DR: Two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction are introduced that proved the global convergence for these schemes.
Journal ArticleDOI
A quasi-Newton algorithm for large-scale nonlinear equations
TL;DR: Numerical results show that the proposed method is competitive with a similar method for large-scale problems.
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.