Adrian Lewis
Cornell University, NY·Mathematics & Statistics
Many tasks in data science, machine learning and engineering come down to optimization: finding the best settings of a model by repeatedly improving a guess. Today's problems are often huge.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
optimization
semi-algebraic geometry
Lojasiewicz inequality
- Grants
- 1 known grant, through Aug 2027
What they work on
- 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.
- Analyze condition measures of nonsmoothness and nonconvexity in Lipschitz optimization to explain the near-linear convergence of popular heuristics, using path-based analysis and distributional derivatives.
- Design new algorithms, guided by these condition measures, that are fast and intuitive enough for machine learning, high-dimensional statistics, imaging science and systems control.
More about the research
Many are also nonsmooth (they have sharp corners) or nonconvex (they have many valleys), and popular methods often work well in practice without any proof that they will. This project uses the mathematical structure built into real problems to design and analyze optimization algorithms that are both fast and reliable.
Why it matters
Machine learning, statistics, imaging science and robust control engineering all rely on optimization methods, yet many widely used methods lack proven guarantees. Rigorous analysis and new algorithms could give practitioners faster methods they can trust on large, irregular problems, including data such as probability distributions and evolutionary trees.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Frank Curtis
Lehigh University, PA·Mathematics & Statistics
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.
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.
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
Cornell University: 37 labs on PI Pages, $1.6B a year on research, 537 research doctorates a year.
Reach out
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