We study the complexity of approximating the multimarginal optimal transport (MOT)
distance, a generalization of the classical optimal transport distance, considered here …

We present a general technique for the analysis of first-order methods. The technique relies
on the construction of a duality gap for an appropriate approximation of the objective …

Nonconvex optimization is central in solving many machine learning problems, in which
block-wise structure is commonly encountered. In this work, we propose cyclic block …

Alternating minimization (AM) procedures are practically efficient in many applications for
solving convex and non-convex optimization problems. On the other hand, Nesterov's …

Alternating minimization (AM) optimization algorithms have been known for a long time and
are of importance in machine learning problems, among which we are mostly motivated by …

Block coordinate descent is an optimization paradigm that iteratively updates one block of
variables at a time, making it quite amenable to big data applications due to its scalability …

First-order methods for solving convex optimization problems have been at the forefront of
mathematical optimization in the last 20 years. The rapid development of this important class …

Coordinate descent methods are popular in machine learning and optimization for their
simple sparse updates and excellent practical performance. In the context of large-scale …

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy
to obtain scalable first-order methods. However, despite their wide use in practice, cyclic …

The smoothness of graph signals has found desirable real applications for processing
irregular (graph-based) signals. When the latent sources of the mixtures provided to us as …