An extended gradient method for smooth strongly convex functions

Abstract

This paper considers an extended gradient method with fixed step size applied to the centralized and decentralized strongly convex and smooth functions. Firstly, the range of step size is derived to guarantee that the function value generated by the extended gradient method converges to the optimal solution at a sublinear rate. Then, we further show that the iterate sequences converge to the optimal solution at a linear rate for the centralized and decentralized problems. Finally, we demonstrate the efficiency of the proposed extended gradient method in numerical experiments.