Author

Ohad Shamir

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Preprint Sep 2026

A Simple Complexity Lower Bound for Solving $Ax=b$

In this note, we provide a short and direct proof that approximately solving $Ax=b$ to relative error $\varepsilon$, where $A$ has condition number $\kappa$ and unrestricted dimension, requires $\Omega(\kappa\log(1/\varepsilon))$ matrix-vector multiplications in the worst case, even for randomized algorithms. This esse...

Ohad Shamir · 0 citations

Jul 2026

Stronger Memory-Query Tradeoffs for Convex Optimization: The Limitations of Subquadratic Memory

This work proves two lower bounds for the first order oracle complexity of minimizing a $d$-dimensional $1$-Lipschitz convex function over the unit ball with $m$ bits of memory and is the first to show a sharp oracle complexity phase transition around $m\approx d^2$.

Michael Menart, Aleksandar Nikolov, Ohad Shamir · arXiv.org · 0 citations