Optimizing problems with group sparsity

Abstract

A class of problems of relatively recent interest and of diverse practical applications, yet difficult to analyze and solve, is the minimization of an lower bounded continuously differentiable function over a disjoint block separable set, involving a penalty and/or constraint that result in the sparsity of such blocks. This project aims to explore this theme from the perspective of the recent methodology and theory presented in the article ''Optimization problems involving group sparsity terms'' by Amir Beck and Nadav Hallak \cite{beck2018} in order to compare approaches and develop insights and tools for the treatment of relevant problems in areas such as graph theory and investments. Particularly, concepts such as proximal mappings (in convex optimization), hierarchy and the necessity of certain optimality conditions will be treated in this context, in addition to the elaboration of efficient algorithms and the reproduction of results obtained in the base reference.