Andrei Draganescu
University of Maryland-Baltimore County, MD·Mathematics & Statistics
Many problems in science and engineering come down to finding the best design or the best set of parameters. Examples include shaping a part, planning radiation therapy, or training an AI model.
- Fields
Mathematics & Statistics
Computer Science
- Topics
non-convex optimization
numerical optimization
first-order methods
- Grants
- 1 known grant, through May 2027
What they work on
- Develop low-rank gradient flow (LRGF), a first-order optimization method that builds quadratic approximations with low-rank Hessians and computes their gradient flow exactly, ending each step with a Wolfe-condition line search.
- Analyze the global convergence and convergence rates of LRGF, and how to construct its low-rank models efficiently.
- Accelerate LRGF with a multilevel approach based on reduced-order models.
- Apply LRGF to maximum likelihood estimation, optimization of hyperbolic partial differential equations, and deep neural network training.
More about the research
Often the landscape of possible solutions has many valleys, and an algorithm can get stuck in a poor one instead of finding a good one. These are called non-convex optimization problems, and they challenge many standard algorithms. This project develops a new method designed to slip past such poor solutions more efficiently.
Why it matters
Better algorithms for non-convex optimization could help a wide range of applications, including computer-aided shape and topology design, radiation therapy planning, manufacturing process optimization, inverse problems, statistics, and AI model training. Open software would let others reproduce the results and use the methods.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Yuhua Zhu
University of California-Los Angeles, CA·Mathematics & Statistics
Develop a consensus-based interacting particle method, where many searchers share information to agree on the best point, for nonconvex optimization problems with equality constraints.
Haomin Zhou
Georgia Institute of Technology, GA·Mathematics & Statistics
Establish parameterized Wasserstein sub-manifolds, which represent evolving probability distributions through a neural network's parameters via a push-forward map and pullback metric, and develop their mathematical foundations.
Roummel Marcia
University of California-Merced, CA·Mathematics & Statistics
Extend deep unrolling networks for signal recovery and image reconstruction by training them with quasi-Newton optimization methods that exploit previous iterates and gradients.
The school
University of Maryland-Baltimore County: 7 labs on PI Pages, $151M a year on research, 90 research doctorates a year.
Reach out
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