Abstract The Alternating Direction Method of Multipliers (ADMM) has been introduced in
1974 and has been used (and still is) under the name of ALG2 for the numerical solution of …

In image processing, the Rudin–Osher–Fatemi (ROF) model [L. Rudin, S. Osher, and E.
Fatemi, Phys. D, 60 (1992), pp. 259–268] based on total variation (TV) minimization has …

Orthogonality constrained problems are widely used in science and engineering. However,
it is challenging to solve these problems efficiently due to the non-convex constraints. In this …

Recently augmented Lagrangian method has been successfully applied to image
restoration. We extend the method to total variation (TV) restoration models with non …

In this paper, we consider a class of optimization problems with orthogonality constraints, the
feasible region of which is called the Stiefel manifold. Our new framework combines a …

During a very large part of his career the author of this book has been interested in the
application of variational methods to problems from science and engineering, particularly …

Variational methods are commonly used to solve noise removal problems. In this paper, we
present an augmented Lagrangian-based approach that uses a discrete form of the L^1 …

We propose a class of multipliers correction methods to minimize a differentiable function
over the Stiefel manifold. The proposed methods combine a function value reduction step …

This paper investigates links between the eigenvalues and eigenfunctions of the Laplace-
Beltrami operator, and the higher Cheeger constants of smooth Riemannian manifolds …

Our main goal in this chapter is to discuss the application of Alternating Direction Methods of
Multipliers (ADMM) to the numerical solution of non-convex (and possibly non-smooth) …