A New Conjugate Gradient for Unconstrained Optimization Based on Step Size of Barzilai and Borwein

Abstract

In this paper, a new formula of is suggested for conjugate gradient method of solving unconstrained optimization problems based on step size of Barzilai and Borwein. Our new proposed CG-method has descent condition, sufficient descent condition and global convergence properties. Numerical comparisons with a standard conjugate gradient algorithm show that this algorithm very effective depending on the number of iterations and the number of functions evaluation.

Keywords

• Unconstrained optimization
• Conjugate gradient
• Descent condition
• Sufficient descent condition
• Barzilai and Borwein step size
• Global convergence