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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

David Gutman, Wm Michael Barnes Department of Industrial & Systems Engineering
Tangent Subspace Descent on Quotient Manifolds


The tangent subspace descent method (TSD) extends the coordinate descent algorithm to manifold domains. The key insight underlying TSD is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. The core principle behind ensuring convergence of TSD for smooth functions is the appropriate choice of subspace at each iteration. In this talk, we will show that it is always possible to appropriately pick such subspaces on the broad class of manifolds known as quotient manifolds. This class includes Grassmannians, flag manifolds, and the positive definite manifold when endowed with an appropriate geometry. As a result of our developments we derive new and efficient methods for large-scale optimization on these domains.