A new gradient method via least change secant update

• Main Authors: Leong, Wah June, Abu Hassan, Malik
• Format: Article
• Language: English
• Published: Taylor & Francis 2011
• Online Access: http://psasir.upm.edu.my/id/eprint/12746/1/A%20new%20gradient%20method%20via%20least%20change%20secant%20update.pdf; http://psasir.upm.edu.my/id/eprint/12746/

The Barzilai–Borwein (BB) gradient method is favourable over the classical steepest descent method both in theory and in real computations. This method takes a ‘fixed’ step size rather than following a set of line search rules to ensure convergence. Along this line, we present a new approach for the two-point approximation to the quasi-Newton equation within the BB framework on the basis of a well-known least change result for the Davidon–Fletcher–Powell update and propose a new gradient method that belongs to the same class of BB gradient method in which the line search procedure is replaced by a fixed step size. Some preliminary numerical results suggest that improvements have been achieved.