5 research outputs found
Fast primal-dual algorithms via dynamics for linearly constrained convex optimization problems
By time discretization of a primal-dual dynamical system, we propose an
inexact primal-dual algorithm, linked to the Nesterov's acceleration scheme,
for the linear equality constrained convex optimization problem. We also
consider an inexact linearized primal-dual algorithm for the composite problem
with linear constrains. Under suitable conditions, we show that these
algorithms enjoy fast convergence properties. Finally, we study the convergence
properties of the primal-dual dynamical system to better understand the
accelerated schemes of the proposed algorithms. We also report numerical
experiments to demonstrate the effectiveness of the proposed algorithms
Fast convergence of primal-dual dynamics and algorithms with time scaling for linear equality constrained convex optimization problems
We propose a primal-dual dynamic with time scaling for a linear equality
constrained convex optimization problem, which consists of a second-order ODE
for the primal variable and a first-order ODE for the dual variable. Without
assuming strong convexity, we prove its fast convergence property and show that
the obtained fast convergence property is preserved under a small perturbation.
We also develop an inexact primal-dual algorithm derived by a time
discretization, and derive the fast convergence property matching that of the
underlying dynamic. Finally, we give numerical experiments to illustrate the
validity of the proposed algorithm