A Liu-Storey-type conjugate gradient method for unconstrained minimization problem with application in motion control

Abstract

Conjugate gradient methods have played a vital role in finding the minimizers of large-scale unconstrained optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. Based on the Liu-Storey conjugate gradient method, in this paper, we present a Liu-Storey type method for finding the minimizers of large-scale unconstrained optimization problems. The direction of the proposed method is constructed in such a way that the sufficient descent condition is satisfied. Furthermore, we establish the global convergence result of the method under the standard Wolfe and Armijo-like line searches. Numerical findings indicate that our presented approach is efficient and robust in solving large-scale test problems. In addition, an application of the method is explored.

Keywords

• Unconstrained optimization
• Conjugate gradient method
• Line search
• Global convergence