math.OC · 2026-09-28 · No. 127

Optimization and Control, 2026-09-28.

2 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Retraction-Based Gradient Projection Algorithms on Manifolds

    Conglong Xu, Hao Wu

    math.OC · cs.LG

    We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an...

    arxiv.org/abs/2609.30885 · PDF

  2. 02

    Tight Stochastic Condition-Number Dependence in Nonconvex-Strongly-Concave Minimax Optimization

    Qihao Zhou

    math.OC · cs.LG

    We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization. For jointly $L$-smooth objectives with dual strong-concavity parameter $μ$, we prove a lower bound that matches the SAPD+ upper bound under the same Moreau-envelope stationarity criterion and the same primal-dual initialization gap. Specifically, when $σ\ge\varepsilon$, the worst-case...

    arxiv.org/abs/2609.30877 · PDF

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