# Collaborative Research: Gradient-free optimization of matrix functions

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · Colorado School of Mines (CO) · $150,000

## Abstract

Artificial intelligence models typically reduce to optimization problems: find the best solution according to a problem-specific metric. Sometimes, the nature of the problems means that the standard calculus-based tools cannot be applied. This setting is known as gradient-free optimization, and is particularly relevant for small businesses, academic research groups, and public-sector organizations that lack large-scale computing infrastructure yet still need to fine-tune machine learning models or optimize complex simulations. This project develops new mathematical and computational tools that make gradient-free optimization dramatically more efficient by exploiting hidden low-dimensional structure in these problems. This will lower the computational barrier to entry for a broad range of users. The project will train PhD students in these interdisciplinary methods, produce openly available software, and develop instructional materials connecting linear algebra to modern deep learning.

Gradient-free optimization (GFO) has deep theoretical foundations, yet remains poorly understood in high dimensions. This project will establish mathematical and algorithmic tools that break worst-case GFO barriers by exploiting structure in matrix-valued gradients. Algorithms for objective functions whose gradients exhibit various kinds of low intrinsic dimensionality, such as sparsity, low rank, or sparsity-plus-low-rank will be developed. These gradient estimation techniques will be wrappe

## Key facts

- **NSF award ID:** 2608659
- **Awardee organization:** Colorado School of Mines (CO)
- **SAM.gov UEI:** JW2NGMP4NMA3
- **PI:** Daniel McKenzie
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Artificial Intelligence (AI), Machine Learning Theory, COMPUTATIONAL SCIENCE & ENGING
- **Estimated total:** $150,000
- **Funds obligated:** $150,000
- **Transaction type:** Standard Grant
- **Period:** 07/01/2026 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2608659

## Citation

> US National Science Foundation, Award 2608659, Collaborative Research: Gradient-free optimization of matrix functions. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2608659. Licensed CC0.

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