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
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Book
Machine Learning : A Probabilistic Perspective
TL;DR: This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach, and is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
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Nonmonotone Spectral Projected Gradient Methods on Convex Sets
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A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
Hongchao Zhang,William W. Hager +1 more
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References
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A class of nonmonotone stabilization methods in unconstrained optimization
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Qn-like variable storage conjugate gradients*
Albert G. Buckley,A. LeNir +1 more
TL;DR: A new combined CG-QN algorithm which can use whatever storage is available and is presented to demonstrate that the new algorithm is never worse than CONMIN and that it is almost always better if even a small amount of extra storage is provided.