Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization - Ling, Mei Mei (2015)
This thesis focuses on solving conjugate gradient methods for large-scale uncon- strained optimization problems. The main objective of this study is to propose some modifications to the standard conjugate gradient methods so that its search direction satisfies the sufficient descent and the boundedness condition. These two conditions appear to be a natural way of guaranteeing convergence for the conjugate gradient methods. We also propose some techniques for improving the conjugate gradient methods. The techniques in consideration include scaling parameters proposed by Oren and Luenberger, preconditioner suggested by Powell and memoryless symmetric rank one. In addition, the modified scaled conjugate gradient method is also implemented using nonmonotone line search. The convergence results for all of the modified conjugate gradient methods are also established. To validate the usefulness of our proposed improvement strategies, numerical ex- periments on a set of standard test problems were performed and presented. The results showed that our proposed methods can be good alternatives to the conju- gate gradient method in solving large-scale unconstrained optimization problems.