The Barzilai and Borwein Gradient Method with Nonmonotone Line Search for Nonsmooth Convex Optimization Problems

Abstract

The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient.

Keywords:

• nonsmooth convex minimization
• spectral gradient
• nonmonotone technique
• global convergence

AMS Subject Classification:

• 90C26