Please use this identifier to cite or link to this item: https://doi.org/10.1007/BF00940534
Title: Vectorization of conjugate-gradient methods for large-scale minimization in meteorology
Authors: Navon, I.M.
Phua, P.K.H. 
Ramamurthy, M.
Keywords: Conjugate-gradient methods
direct minimization
large-scale minimization
meteorological problems
vectorization
Issue Date: Jul-1990
Source: Navon, I.M., Phua, P.K.H., Ramamurthy, M. (1990-07). Vectorization of conjugate-gradient methods for large-scale minimization in meteorology. Journal of Optimization Theory and Applications 66 (1) : 71-93. ScholarBank@NUS Repository. https://doi.org/10.1007/BF00940534
Abstract: During the last few years, conjugate-gradient methods have been found to be the best available tool for large-scale minimization of nonlinear functions occurring in geophysical applications. While vectorization techniques have been applied to linear conjugate-gradient methods designed to solve symmetric linear systems of algebraic equations, arising mainly from discretization of elliptic partial differential equations, due to their suitability for vector or parallel processing, no such effort was undertaken for the nonlinear conjugate-gradient method for large-scale unconstrained minimization. Computational results are presented here using a robust memoryless quasi-Newton-like conjugate-gradient algorithm by Shanno and Phua applied to a set of large-scale meteorological problems. These results point to the vectorization of the conjugate-gradient code inducing a significant speed-up in the function and gradient evaluation for the nonlinear conjugate-gradient method, resulting in a sizable reduction in the CPU time for minimizing nonlinear functions of 104 to 105 variables. This is particularly true for many real-life problems where the gradient and function evaluation take the bulk of the computational effort. It is concluded that vector computers are advantageous for largescale numerical optimization problems where local minima of nonlinear functions are to be found using the nonlinear conjugate-gradient method. © 1990 Plenum Publishing Corporation.
Source Title: Journal of Optimization Theory and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/99461
ISSN: 00223239
DOI: 10.1007/BF00940534
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