Analysis of versions of relaxed inertial projection and contraction method

• DOI: 10.1016/j.apnum.2021.02.004
• Publication Date: 2021-02-09T20:24:35Z
• Authors: Yekini Shehu; Lulu Liu; Xuewen Mu; Qiao-Li Dong
• Keywords: Projection method; Weak convergence; Contraction mapping

Abstract In this paper, we first study a relaxed inertial projection and contraction method for variational inequalities to obtain weak convergence results under standard assumptions in Hilbert spaces. Next, we propose another inertial projection and contraction method for which the inertial factor θ is chosen in [ 0 , 1 ] with θ = 1 possible. Weak and linear convergence are obtained for this second proposed method. As far as we know, the choice θ = 1 has not been considered before in the literature for inertial projection and contraction method. Finally, we give some numerical illustrations of our methods.