A first-order multigrid method for bound-constrained convex optimization
This work provides a scalable first-order multigrid solver for bound-constrained convex optimization, relevant for large-scale problems arising from discretized infinite-dimensional problems.
The paper proposes a first-order multigrid method for bound-constrained convex optimization problems, achieving computational efficiency without second derivatives. Numerical experiments demonstrate the method's effectiveness for large-scale problems.
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (possibly) a single equality constraint. As our aim is to target large-scale problems, we want to avoid computation of second derivatives of the objective function, thus excluding Newton like methods. We propose a smoothing operator that only uses first-order information and study the computational efficiency of the resulting method.