On projected alternating BB methods for variational inequalities. (3rd April 2021)

• Record Type: Journal Article
• Authors: Qu, Yunfei; Tong, Wanbin; He, Hongjin; Liou, Yeong-Cheng
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 827
• Page End: 846
• Publication Date: 2021-04-03
• Subjects: Projection method -- BB step size -- variational inequality problem -- Complementarity problem -- image deblurring; 65K05 -- 90C30 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1721495
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The Barzilai–Borwein (BB) step size initially proposed in the context of unconstrained optimization has become one of the most popular step choices for gradient-based methods in the optimization community. It is well-known that the powerful variational inequality can be used to characterize the first-order optimality condition of constrained optimization problems. However, a variational inequality problem is not always equivalent to a constrained optimization problem. In this paper, we follow the spirit of BB step size and propose a projection method with alternate BB step size for general variational inequalities. Although the global convergence is established under some strong conditions, a series of computational experiments on nonlinear complementarity problems, image deblurring problems and generalized Nash equilibrium problems demonstrate that the proposed almost-parameter-free projection method is more efficient than some existing state-of-the-art projection methods in the literature.