A New Three–Term Conjugate Gradient Method with Descent Direction for Unconstrained Optimization

Abstract

In this paper, we propose a three–term PRP–type conjugate gradient method which always satisfies the sufficient descent condition independently of line searches employed. An important property of our method is that its direction is closest to the direction of the Newton method or satisfies conjugacy condition as the iterations evolve. In addition, under mild condition, we prove global convergence properties of the proposed method. Numerical comparison illustrates that our proposed method is efficient for solving the optimization problems.

Keywords:

• unconstrained optimization
• conjugate gradient method
• sufficient descent con- dition
• global convergence

AMS Subject Classification:

• 49M37
• 65K05
• 90C53