Primal–dual hybrid gradient (PDHG) and alternating direction method of multipliers (ADMM) are popular first-order optimization methods. They easy to implement have diverse applications. As methods, however, they sensitive problem conditions can struggle reach the desired accuracy. To improve their performance, researchers proposed techniques such as diagonal preconditioning inexact subproblems....

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by subproblem in each iteration. We show that can achieve optimal rate of convergence variety VI problems much simpler way than existing approaches. then introduce sto...