An alternating direction method of multipliers with the BFGS update for structured convex quadratic optimization

The alternating direction method of multipliers (ADMM) is an effective for solving convex problems from a wide range fields. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it expensive or impossible to obtain exact solutions subproblems. To overcome difficulty, some proximal terms are added This class methods typically original subproblem approximately and hence requires more iterations. fact urges us consider that special term can yield better results than ADMM. In this paper, we propose whose regularization matrix generated by BFGS update (or limited memory BFGS) at every iteration. These types matrices use second-order information objective function. convergence proposed proved under certain assumptions. Numerical presented demonstrate effectiveness