Feasibility models can be found everywhere in optimization and involve finding a point in the intersection of a collection (possibly infinite) of sets. The focus of most of the theory for feasibility models is on the case where the intersection is nonempty. But in applications, one encounters infeasible problems more often than might be expected. We examine a few high-profile instances of inconsistent feasibility and demonstrate the application of a recently established theoretical framework for proving convergence, with rates, of some elementary algorithms for inconsistent feasibility.
joint work with Marc Teboulle
In this talk we consider the nonnegative matrix factorization (NMF) problem with a particular focus on its sparsity constrained variant (SNMF). Of the wide variety of methods proposed for NMF, only few are applicable for SNMF and guarantee global convergence to a stationary point. We propose several additional, globally convergent methods, which are applicable to SNMF. Some are extensions of existing state of the art methods, while others are genuine proximal methods that tackle non standard decompositions of NMF, leading to subproblems lacking a Lipschitz continuous gradient objective.
Proximal based methods are nowadays starring in optimization algorithms, and are effectively used in a wide spectrum of applications. This talk will present some recent work on the impact of the proximal framework for composite minimization, with a particular focus on convergence analysis and applications.