Patrick Combettes
North Carolina State University, NC·Mathematics & Statistics
Many modern computing problems are enormous and noisy: training machine learning models, reconstructing medical images, processing signals, interpreting geophysical data. Their mathematical models involve huge numbers of variables and random perturbations, and the algorithms used to solve them often make random choices to save effort.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
stochastic algorithms
convex optimization
convex feasibility
- Grants
- 1 known grant, through Jun 2028
What they work on
- Develop a geometric framework unifying stochastic algorithms for convex feasibility, best approximation, convex optimization, fixed-point, variational inequality and monotone inclusion problems, and use it to design new methods.
- Establish common principles for the asymptotic behavior of algorithms that rely on stochastic operator approximations, random coordinate updates and random operator activations.
- Analyze randomized solution methods for convex feasibility problems and for multivariate systems of structured monotone inclusions, then extend the analysis beyond the convex and monotone setting.
- Apply the resulting theory and algorithms to signal processing, machine learning, inverse problems, statistical biology and medical imaging.
More about the research
This project asks a foundational question: what geometric principles explain when such randomized algorithms converge, and how can those principles guide the design of better ones?
Why it matters
Randomized algorithms with reliable convergence guarantees could speed up large computational tasks in medical imaging, signal processing, machine learning and geophysics. Clearer design principles may help researchers and engineers tackle huge, noisy problems where current methods are slow or lack theoretical support.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Nikhil Bansal
University of Michigan, MI·Computer Science
Determine how many iterations the interior-point method, a standard algorithm for large optimization problems, needs in the worst case, on average and on sparse inputs, to understand its true complexity.
Weilin Li
CUNY City College, NY·Mathematics & Statistics
Construct objective functions for continuous parameter estimation whose informative minima lie close to the true parameters and have large basins of attraction, so standard local optimization methods can locate them efficiently.
Andrei Draganescu
University of Maryland-Baltimore County, MD·Mathematics & Statistics
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.
The school
North Carolina State University: 40 labs on PI Pages, $717M a year on research, 603 research doctorates a year.
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