A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria

2025/08/26 by Zheng, Zhong, Yu, Xin, Ma, Shiqian +1 · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2508.19234

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. We establish convergence guarantees and show that IManPL achieves the best first-order oracle complexity for solving this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches.

Citations

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• An inexact variable metric proximal linearization method for composite optimization on manifolds

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