math.OC · 2026-09-29 · No. 128

Optimization and Control, 2026-09-29.

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

    Learned Preconditioning for a Primal-Dual Interior-Point Method

    Abhinav Madabhushi, Jialin Liu, Minxin Zhang

    math.OC · cs.LG

    Interior-point methods (IPMs) are among the most widely used algorithms for constrained optimization, yet their Newton-based search directions require costly second-order information and large linear-system solves. Learning to optimize offers cheaper updates learned from data, but the singular behavior of logarithmic barriers near constraint boundaries makes IPMs highly sensitive to perturbations, complicating both warm starting and learning...

    arxiv.org/abs/2609.35665 · PDF

  2. 02

    Convex Optimization Is Free When Accuracy Is Expensive

    Arthur Paing, Arthur Jacot

    math.OC · cs.LG · stat.ML

    This paper studies convex optimization when the gradient cannot be evaluated exactly, but only approximated by a hierarchy of algorithms whose compute grows like $δ^{-γ}$ in the accuracy $δ$. When $γ>2$, falling into the Harder-Than-Monte-Carlo (HTMC) regime, the price of accuracy outruns the variance reduction that Monte Carlo would buy and we show that minimizing a loss function costs no more, up to a factor depending only on $γ$, than a...

    arxiv.org/abs/2609.35418 · PDF

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