NSF Computational Mathematics program awards grant to Prof. Li

Assistant Professor Weilin Li received a National Science Foundation grant from the Computational Mathematics program of the Division of Mathematical Sciences. The three-year $215,000 award "A rigorous optimization framework for high-resolution parameter estimation on the continuum" begins September 2026. The award supports Prof. Li's work on understanding and improving optimization in environments with noisy data.

This project develops a general optimization framework for continuous parameter estimation by constructing objective functions with provably favorable geometric properties. The research seeks to establish conditions under which informative minima lie close to the true parameters, possess large basins of attraction, and can be located efficiently using local optimization methods, while spurious minima remain shallow and can be avoided through a rejection strategy. A central goal is to show that these properties are governed by an underlying correlation kernel, providing a unified theoretical framework for a broad class of parameter estimation problems. The framework will be analyzed and validated through three representative applications: wave-based imaging, sparse decompositions, and reconstruction from noisy random rotations. For each application, the project will establish theoretical recovery guarantees and develop computational algorithms that exploit the underlying problem structure to achieve high-resolution parameter estimation.

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