Adrian Lewis

About

Adrian S. Lewis is the Samuel B. Eckert Professor of Engineering at Cornell University in the School of Operations Research and Information Engineering. He received his B.A., M.A., and Ph.D. degrees from Cambridge University, U.K., and has held faculty positions at the University of Waterloo and Simon Fraser University before joining Cornell in 2004. His research focuses on nonsmooth optimization and variational analysis, with particular interest in the mathematical theory underlying these areas and their practical applications in science and engineering. His work includes the design and analysis of computational algorithms for nonsmooth optimization, especially problems involving eigenvalues such as robust control and pseudospectral sensitivity. Recently, his research has expanded into semi-algebraic geometry as a model for generic structure in nonsmooth optimization, blending variational analysis, classical mathematics, numerical computation, and applied modeling.

Research topics

• Artificial Intelligence
• Computer Science
• Mathematics
• Algorithm
• Mathematical optimization

Selected publications

• Gradient Sampling Methods for Nonsmooth Optimization

  Springer eBooks · 2020 · 67 citations

  PublisherDOI

• Partial Smoothness and Constant Rank

  SIAM Journal on Optimization · 2022-03-01 · 10 citations

  article1st authorCorresponding

  In optimization, the notion of a partly smooth objective function is powerful for applications in algorithmic convergence and postoptimality analysis, and yet is complex to define. A shift in focus to the first-order optimality conditions reduces the concept to a simple constant-rank condition. In this view, partial smoothness extends to more general variational systems, encompassing in particular the saddlepoint operators underlying popular primal-dual splitting algorithms. For a broad class of…

  PublisherDOI

• Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimization

  SIAM Journal on Optimization · 2023-01-17 · 7 citations

  articleSenior author

  .For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable, and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergence guarantees that are sublinear relative to the cumulative number of gradient evalu…

  PublisherDOI

• The Cost of Nonconvexity in Deterministic Nonsmooth Optimization

  Mathematics of Operations Research · 2023-11-29 · 6 citations

  articleSenior author

  We study the impact of nonconvexity on the complexity of nonsmooth optimization, emphasizing objectives such as piecewise linear functions, which may not be weakly convex. We focus on a dimension-independent analysis, slightly modifying a 2020 black-box algorithm of Zhang-Lin-Jegelka-Sra-Jadbabaie that approximates an ϵ-stationary point of any directionally differentiable Lipschitz objective using [Formula: see text] calls to a specialized subgradient oracle and a randomized line search. Seeking…

  PublisherDOI

• Basic Convex Analysis in Metric Spaces with Bounded Curvature

  SIAM Journal on Optimization · 2024-01-19 · 3 citations

  article1st authorCorresponding

  .Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however, extensions are more challenging. Nonetheless, in Alexandrov spaces with curvature bounded above (but possibly positive), we develop several basic building blocks. We define subgradients via projection and the normal cone, prove their existence, and relate them to the classical affine minorant property. Then, in what…

  PublisherDOI

Recent grants

• Variational Analysis for Practical Optimization

  NSF · $388k · 2008–2012

• Semi-Structured Optimization: Geometry and Nonsmooth Algorithms

  NSF · $351k · 2020–2024

• Geometry in nonsmooth optimization

  NSF · $413k · 2012–2016

Frequent coauthors

• Jonathan M. Borwein

  University of Newcastle Australia

  69 shared

• Dmitriy Drusvyatskiy

  41 shared

• Michael L. Overton

  38 shared

• James V. Burke

  22 shared

• Aris Daniilidis

  TU Wien

  17 shared

• A. D. Ioffe

  Technion – Israel Institute of Technology

  12 shared

• Adriana Nicolae

  8 shared

• Genaro López-Acedo

  Universidad de Sevilla

  7 shared

Awards & honors

• 1995 Aisenstadt Prize
• 2003 Lagrange Prize
• 2005 Outstanding Paper Prize from SIAM
• Section Lecturer at the 2014 International Congress of Mathe…

Similar researchers at Cornell University

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• Robert A. Jarrowh-68
• Andrea Lodih-53