Winner
David H. Gutman (Department of Industrial, Manufacturing, and Systems Engineering, Texas Tech University, USA) and Nam Ho-Nguyen (The Business School, The University of Sidney, Australia) for their joint paper entitled “Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds.”
Citation
This paper proposes the new tangent subspace descent (TSD) method, which opens up new and exciting research directions in both manifold optimization and coordinate descent methods by generalizing the classical Euclidean coordinate descent method to Riemannian optimization over a manifold. This is a highly nontrivial generalization because in the manifold setting, there is no global coordinate system. As such, two fundamental challenges arise: a) how to generalize the notions of coordinates and blocks of variables, and b) how to select blocks to guarantee fast convergence of the method. The authors of this paper made the crucial observation that the tangent space to the manifold at each point can be decomposed into a collection of subspaces. To account for the fact that the tangent spaces generally change from one point to another, they made use of parallel transport to identify tangent vectors at different points. Consequently, the proposed TSD method performs “coordinate descent” in the manifold setting by projecting the Riemannian gradient onto one of the subspaces. The authors identified two conditions on the selection of the tangent subspace decomposition and established convergence rates of the proposed method under these conditions. Furthermore, they showed that it is possible to obtain a desired decomposition without computing the parallel transport. In summary, the development of the innovative and groundbreaking TSD method in this paper makes it truly deserving of the INFORMS Optimization Society Prize for Young Researchers.
Prize committee
George Lan (chair), Frank Curtis, Jim Luedtke, and Rahul Mazumder