Inertial proximal strictly contractive Peaceman–Rachford splitting method with an indefinite term for convex optimization

Abstract

We consider an inertial proximal strictly contractive Peaceman–Rachford splitting method (abbreviated as IPSCPRSM) with an indefinite proximal term for solving convex optimization problems with linear constraints. With the aid of variational inequality, proximal point method and fundamental inequality, we prove global convergence of the proposed method and analyze iteration complexity in the best function value and feasibility residues. The experimental results demonstrate the efficiency of the inertial extrapolation step and the indefinite proximal term even compared with the state-of-the-art methods.