# Lower Bound for Randomized First Order Convex Optimization

arXiv: https://arxiv.org/abs/1709.03594 · HTML: https://mlsanity.com/paper/1709.03594/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2017.

## Built on by (most cited first, 9 of 9)

- [Oracle Complexity in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2104.06763/) (2021)
- [Efficient Convex Optimization Requires Superlinear Memory](https://mlsanity.com/paper/2203.15260/) (2022)
- [Query lower bounds for log-concave sampling](https://mlsanity.com/paper/2304.02599/) (2023)
- [On the Complexity of Finding Small Subgradients in Nonsmooth Optimization](https://mlsanity.com/paper/2209.10346/) (2022)
- [The Minimax Complexity of Distributed Optimization](https://mlsanity.com/paper/2109.00534/) (2021)
- [Quadratic Memory is Necessary for Optimal Query Complexity in Convex Optimization: Center-of-Mass is Pareto-Optimal](https://mlsanity.com/paper/2302.04963/) (2023)
- [Accelerated Gradient Algorithms with Adaptive Subspace Search for Instance-Faster Optimization](https://mlsanity.com/paper/2312.03218/) (2023)
- [Complexity Bounds for Smooth Multiobjective Optimization](https://mlsanity.com/paper/2509.13550/) (2025)
- [Optimal Stochastic Bilevel Optimization with First-Order Oracles](https://mlsanity.com/paper/2610.01843/) (2026)

## Abstract (arXiv)

We provide an explicit construction and direct proof for the lower bound on the number of first order oracle accesses required for a randomized algorithm to minimize a convex Lipschitz function.