A modified subgradient extragradient method for solving the variational inequality problem

作者：Dong, Qiao-Li^*; Jiang, Dan; Gibali, Aviv

来源：Numerical Algorithms, 2018, 79(3): 927-940.

DOI：10.1007/s11075-017-0467-x

• Variational inequality
• Extragradient method
• Subgradient extragradient method
• Projection and contraction method

The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. (J. Optim. Theory Appl. 148, 318-335, 2011), replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.

• 出版日期2018-11
• 单位中国民航大学