A new conjugate gradient method with an efficient memory structure

Abstract

A new family of conjugate gradient methods for large-scale unconstrained optimization problems is described. It is based on minimizing a penalty function, and uses a limited memory structure to exploit the useful information provided by the iterations. Our penalty function combines the good properties of the linear conjugate gradient method using some penalty parameters. We propose a suitable penalty parameter by solving an auxiliary linear optimization problem and show that the proposed parameter is promising. The global convergence of the new method is investigated under mild assumptions. Numerical results show that the new method is efficient and confirm the effectiveness of the memory structure.