math.OC · 2026-08-25 · No. 95

Optimization and Control, 2026-08-25.

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

01 — The papers

3 entries
  1. 01

    SGHA: A Single-Loop Fully First-Order Algorithm for Nonconvex-Strongly-Convex Bilevel Optimization

    Zhihao Gu, Qilong Wu, Junchi Yang

    math.OC · cs.LG

    In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving the best-known complexity guarantees typically rely on double-loop, penalty-based procedures. We propose a novel single-loop algorithm based on a constrained reformulation in which lower-level stationarity is imposed as a constraint. Specifically,...

    arxiv.org/abs/2608.23211 · PDF

  2. 02

    CED-EF: Compressed Exact Diffusion with Error Feedback for Multi-Agent Learning

    Sulaiman A. Alghunaim, Kun Yuan

    math.OC · cs.DC

    We study decentralized stochastic optimization over a network of $N$ agents under compressed communication. We propose CED-EF, an exact diffusion-based method with error feedback that directly accommodates biased $δ$-contractive compressors while communicating one compressed model-sized vector per node per iteration. For smooth nonconvex objectives with unbiased stochastic gradients whose variance is bounded by $σ^2$, where $σ\geq0$, we...

    arxiv.org/abs/2608.23013 · PDF

  3. 03

    Mirror descent algorithms with logarithmic barriers

    Alberto De Marchi, Yura Malitsky, Adrien B. Taylor

    math.OC · cs.LG · math.NA

    This work derives convergence guarantees for mirror descent and proximal mirror descent algorithms when a logarithmic barrier is used as a distance-generating function. Standard approaches cannot be applied when the solution lies on the boundary, where the Bregman divergence blows up. We show that, in a specific setting, both methods enjoy an $O(\log k / k)$ rate, which is also tight. In addition, our contributions include: (i) a new...

    arxiv.org/abs/2608.22834 · PDF

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