Open AccessTHE BARZILAI AND BORWEIN GRADIENT METHOD WITH NONMONOTONE LINE SEARCH FOR NONSMOOTH CONVEX OPTIMIZATION PROBLEMS
Author(s) -
Gonglin Yuan,
Zengxin Wei
Publication year - 2012
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2012.661375
Subject(s) - line search , gradient method , mathematics , convergence (economics) , mathematical optimization , proximal gradient methods , minification , regular polygon , line (geometry) , convex optimization , simple (philosophy) , pseudoconvex function , optimization problem , computer science , convex combination , philosophy , geometry , computer security , epistemology , economics , radius , economic growth
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.