A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria

Abstract

This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. Under the stated assumptions, we establish convergence guarantees and an $O({\epsilon }^{-3})$ first-order oracle complexity bound for APG subproblem solves, matching the best-known order for this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches.

arXiv commentThis paper has been accepted for publication in the INFORMS Journal on Optimization