Federal Grant Award Summary

The Colorado School of Mines received a $150,000 Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026 through June 30, 2028. This collaborative research initiative develops mathematical and computational tools for gradient-free optimization (GFO) of matrix functions, addressing a critical gap in optimization methods applicable to organizations lacking large-scale computing infrastructure. The project delivers novel algorithms and techniques that exploit low-dimensional structure—such as sparsity, low rank, and sparsity-plus-low-rank patterns—in matrix-valued gradients to reduce computational barriers for machine learning model tuning and complex simulation optimization across small businesses, academic research groups, and public-sector organizations.

The award supports the development of open-source software, instructional materials connecting linear algebra to modern deep learning, and training for PhD students in these interdisciplinary optimization methods. The project integrates contemporary optimization algorithms with computational linear algebra techniques to enable efficient gradient estimation and matrix operations in gradient-free settings, advancing both theoretical understanding of high-dimensional GFO and practical algorithmic capabilities for practitioners with limited computational resources.