Moslem Zamani In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class … Read more
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
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
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