A self-adaptive projection method with improved step-size for solving variational inequalities

作者：Yan Xihong; Han Deren; Sun Wenyu

来源：Computers & Mathematics with Applications, 2008, 55(4): 819-832.

DOI：10.1016/j.camwa.2007.05.008

• variational inequalities
• self-adaptive
• projection methods
• co-coercive mappings
• global convergence

In this paper, we propose a new projection method for solving variational inequality problems, which can be viewed as an improvement of the method of Han and Lo [D.R. Han, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537], by adopting a new step-size rule. The method is as simple as Han and Lo';s methods [D.R. Hart, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537] and other extra-gradient-type methods, which uses only function evolutions and projections onto the feasible set. We prove that under the condition that the underlying function is co-coercive, the sequence generated by the method converges to a solution of the variational inequality problem globally. Some preliminary Computational results are reported, which illustrated that the new method is more efficient than Han and Lo';s method [D.R. Han, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537].

• 出版日期2008-2
• 单位南京师范大学