A smoothing-aware AdaGrad Riemannian gradient method achieves O(ε^{p-4}) global complexity for non-Lipschitz manifold optimization with p-norm penalties (p in (0,1]), recovering the known O(ε^{-3}) rate when p=1.
arX iv preprint arXiv:2509.08561 (2025)
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MoSSP is a new single-loop stochastic penalty method with Polyak or recursive momentum that achieves O(ε^{-4}) or O(ε^{-3}) oracle complexity for stochastic ε-KKT points in nonconvex constrained DC-regularized problems.
FSIPL is a feasibility-safeguarded inexact proximal linearized method for nonsmooth composite optimization on compact embedded submanifolds, with O(ε^{-2}) complexity, subsequential convergence, and full convergence under a KL assumption.
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An Adaptive Smoothing Algorithm for Non-Lipschitz Optimization on Manifolds with Complexity Guarantees
A smoothing-aware AdaGrad Riemannian gradient method achieves O(ε^{p-4}) global complexity for non-Lipschitz manifold optimization with p-norm penalties (p in (0,1]), recovering the known O(ε^{-3}) rate when p=1.
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MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization
MoSSP is a new single-loop stochastic penalty method with Polyak or recursive momentum that achieves O(ε^{-4}) or O(ε^{-3}) oracle complexity for stochastic ε-KKT points in nonconvex constrained DC-regularized problems.
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An Infeasible Method with Feasibility Safeguard for Nonsmooth Composite Optimization Over Manifolds
FSIPL is a feasibility-safeguarded inexact proximal linearized method for nonsmooth composite optimization on compact embedded submanifolds, with O(ε^{-2}) complexity, subsequential convergence, and full convergence under a KL assumption.