Structured and low-rank optimization algorithms

The goal of the thesis is to develop a novel theoretical and algorithmic framework for structured and low-rank optimization problems. Low-rank, structured models are ubiquitous in machine learning, signal processing and control. Such formulations naturally lead to nonconvex, nonsmooth but highly structured optimization problems. On the methodological side, the aim of the thesis is to develop new, reliable and scalable algorithms with guaranteed convergence properties for such problems. On the theoretical side, the goal is to study structural properties linked to modeling hypotheses that lead to problems which are tractable in the following sense: If properly initialized, the algorithms proposed in the thesis will be guaranteed to converge to a global minimum, despite nonconvexity.