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.
Yuan, G., & Wei, Z. (2012). The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems. Mathematical Modelling and Analysis, 17(2), 203-216. https://doi.org/10.3846/13926292.2012.661375
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
