A new nonmonotone filter Barzilai–Borwein method for solving unconstrained optimization problems

Abstract

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too.

Keywords:

• Barzilai–Borwein gradient method
• filter technique
• nonmonotone technique
• unconstrained optimization
• global convergence

2010 AMS Subject Classifications:

• 65K05
• 90C30
• 90C06