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arXiv · 2508.19234

A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria

Zhong Zheng·Xin Yu·Shiqian Ma·Lingzhou Xue
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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.

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Zhong Zheng, Xin Yu, Shiqian Ma, Lingzhou Xue. 2025-08-26. A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria. https://arxiv.org/abs/2508.19234

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