math.OC · 2026-08-07 · No. 77

Optimization and Control, 2026-08-07.

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

    Muon on the Stiefel Manifold Admits an Exact Closed-Form Update

    Mikhail Solonko, Molozhavenko Alexander, Maxim Rakhuba

    math.OC · cs.LG · math.NA

    We study Muon, a recently proposed matrix-aware optimization method, in the context of the Stiefel manifold. This manifold consists of matrices with orthonormal columns and is ubiquitous in machine learning and scientific computing. Existing extensions of Muon to this manifold rely on heuristic, approximate, or iterative updates with varying computational efficiency. We show that the corresponding Stiefel Muon update admits an exact...

    arxiv.org/abs/2608.06218 · PDF

  2. 02

    On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities

    TaeHo Yoon, Nicolas Loizou

    math.OC · cs.LG

    We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set. Although extragradient is a foundational algorithm for VIPs and its deterministic convergence theory is well developed, its stochastic counterpart remains less understood. Most existing analyses focus on independent-sample SEG (I-SEG) and assume either that the domain is compact or that the variance of the...

    arxiv.org/abs/2608.06182 · PDF

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