Frank Curtis
Lehigh University, PA·Mathematics & Statistics
Many practical problems, such as cleaning up images, training statistical models, or designing robust control systems, come down to optimization: finding the choice of many variables that makes some cost or error as small as possible. Realistic versions of these problems are hard.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
mathematical optimization
nonsmooth optimization
nonconvex optimization
- Grants
- 1 known grant, through Jul 2028
What they work on
- Revisit the basic properties that gradient sampling methods rely on to guarantee convergence, and strengthen them for nonconvex, nonsmooth, locally Lipschitz problems whose function values are corrupted by computational noise.
- Redesign gradient-sampling-based algorithms to handle stochastic (randomly estimated) function and derivative values, such as those coming from simulations or predictions built on partially observed data.
- Develop convergence theories for the redesigned algorithms, showing when and how they reach good solutions despite noise.
- Implement the new noise-tolerant algorithms within the PI's existing optimization software so they can be used on large-scale applied problems.
More about the research
They can involve huge numbers of variables, and their formulas can have sharp corners, called nonsmoothness, where ordinary calculus-based methods struggle. Worse, the cost of a decision often can only be estimated, for example from a computer simulation or a statistical prediction built on partly observed data. Those estimates carry noise, and existing algorithms are not built to handle it reliably.
Why it matters
Engineers and data scientists often must optimize systems whose performance can only be estimated through simulations or partial data, as in image processing, statistical learning, robust control and distance geometry. Algorithms that remain reliable despite noisy estimates could let these users solve larger and more realistic models. Building the methods into existing software could put them in practitioners' hands.
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.
Adrian Lewis
Cornell University, NY·Mathematics & Statistics
Extend Łojasiewicz-type rescaling techniques to analyze the complexity of first-order and active-set algorithms on semi-algebraic problems in hyperbolic, non-Euclidean and infinite-dimensional spaces.
Ebrahim Sarabi
Miami University-Oxford, OH·Mathematics & Statistics
Establish parabolic regularity and twice epi-differentiability for piecewise linear-quadratic composite problems and classes of matrix optimization problems, extending second-order calculus to objectives that are not differentiable in the usual sense.
The school
Lehigh University: 13 labs on PI Pages, $62M a year on research, 99 research doctorates a year.
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