Optimisation Algorithms for Highly Parallel Computer Architectures. The Performance of the Truncated Newton, Conjugate Gradient Algorithm in FORTRAN and ADA

摘要

This project is concerned with the optimization of objective functions F(x) in a large dimensional space R to the n power on highly parallel computers. It has been established that the truncated Newton method introduced by Dembo & Steihang is an efficient method for solving large optimization algorithms on a sequential machine. The truncated Newton method consists of two main steps: 1) the calculation of the function value F(x),, gradient vector g(x) and Hessian matrix H(x) at a sequence of points x to the (k) power. 2) solving the set of linear equations H(x) d = - g(x) approximately for the search direction d.