The exact worst-case convergence rate of the alternating direction method of multipliers

Recently, semidefinite programming performance estimation has been employed as a strong tool for the worst-case performance analysis of first order methods. In this paper, we derive new non-ergodic convergence rates for the alternating direction method of multipliers (ADMM) by using performance estimation. We give some examples which show the exactness of the given bounds. We … Read more

New bounds for nonconvex quadratically constrained quadratic programming

In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. Recently, Zamani has proposed a dual for linearly constrained quadratic programs, where Lagrange multipliers are affine functions. By using this method, we propose two types of bounds for quadratically constrained quadratic pro- grams, quadratic and cubic bounds. For quadratic bounds, we use … Read more

A new dual for quadratic programming and its applications

The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a modified version by restricting the feasible set. This leads to a new bound … Read more