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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Parallelization of a ray tracer using the SANEG algorithm.
Joali Moreno,Brígida Molina +1 more
TL;DR: An alternative parallel version for a ray tracing algorithm is developed, using an spectral approach for non-linear equation (SANEG) to improve computational performance, and results indicated that computational time was reduced by 85%.
Proceedings ArticleDOI
Performance of the Barzilai-Borwein fixed-step optimization approach in non-invasive microwave imaging
TL;DR: In this paper , the performance of the Barzilai-Borwein non-line search descent is investigated as an inversion strategy for solving the nonlinear inverse scattering problem of UWB microwave tomographic imaging.
Theoretical and Numerical Analysis of Optimization Problems with Applications to Continuum Mechanics
TL;DR: In this article, a linear rate of local convergence is deduced for one of the algorithms, which is based solely on gradient information and combines the algorithms designed in the first chapter with an active-set strategy, and a special class of nonsmooth problems, namely minimax problems minx∈Rn F (x), is introduced.
Optimal polynomial feedback laws for finite horizon control problems
TL;DR: In this article , a learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed and the convergence of the method is analyzed, while paying special attention to avoid the use of a global Lipschitz condition on the nonlinearity which describes the control system.
Book ChapterDOI
A Parallel Spectral-Projected-Gradient Method for Optimization in Process Engineering
TL;DR: An adaptation of the algorithm of the Spectral-Projected-Gradient Method in order to achieve an efficient parallel implementation and it is shown that the parallel approach is useful for optimization problems related to process engineering.
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.