Vectorization of conjugate-gradient methods for large-scale minimization in meteorology
During the last few years, conjugate-gradient methods were 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 developed in a paper by \textit{D. F. Shanno} and \textit{K. H. Phua} [ACM Trans. Math. Software 6, 618-622 (1980)] 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 \(10^ 4\) to \(10^ 5\) variables. This is particularly true for many real-life problems where the gradient and function evaluations take the bulk of the computational effort. It is concluded that vector computers are advantageous for large-scale numerical optimization problems where local minima of nonlinear functions are to be found using the nonlinear conjugate-gradient method.
robust memoryless quasi- Newton-like conjugate-gradient algorithm
scientific article; zbMATH DE number 4116310
scientific article