Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose randomized proximal gradient method harnessing underlying structure. We introduce two key components: (i) random subspace algorithm; and (ii) an identification-based sampling of subspaces. Th...

Motion planning is a fundamental problem in autonomous robotics that requires finding path to specified goal avoids obstacles and takes into account robot's limitations constraints. It often desirable for this also optimize cost function, such as length. Formal path-quality guarantees continuously valued search spaces are an active area of research interest. Recent results have proven some samp...