About

Michael L. Overton is the Silver Professor of Computer Science and Mathematics at the Courant Institute of Mathematical Sciences, New York University. His educational background includes a B.Sc. (honors) in Computer Science from the University of British Columbia in 1974, followed by an M.S. and Ph.D. in Computer Science from Stanford University in 1977 and 1979, respectively. His research focuses on numerical computing, control, optimization, and linear algebra software, with recent work including the publication of the second edition of his book on floating point arithmetic. Overton has made significant contributions to the field through his research, teaching undergraduate and graduate courses, and advising PhD and MS students. He has been recognized as a Fellow of SIAM and IMA, and is the author of the book 'Numerical Computing with IEEE Floating Point Arithmetic' and its translation into Spanish. His professional service includes editorial roles on prominent journals such as the IMA Journal of Numerical Analysis, Numerische Mathematik, and Foundations of Computational Mathematics. He has held leadership positions in various organizations, including SIAM, FoCM, the Fields Institute, CMS, PIMS, and the Simons Foundation. Overton has delivered numerous lectures worldwide, organized key conferences, and participated in various advisory boards, reflecting his active engagement in advancing computational mathematics and numerical analysis.

Research topics

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

Selected publications

• Numerical Computing with IEEE Floating Point Arithmetic: Including One Theorem, One Rule of Thumb, and One Hundred and Six Exercises, Second Edition

  Society for Industrial and Applied Mathematics eBooks · 2025-01-01

  book1st authorCorresponding
  PublisherDOI

• On the Subdifferentiability of functions of a Matrix Spectrum II: Subdifferential Formulas

  2024-12-10

  book-chapterSenior author

  In this paper, we develop a few of the variational properties of the spectral radius, ρ, and the spectral abscissa, α, for the analytic matrix valued mapping https://www.w3.org/1998/Math/MathML" display="inline"> A : ℂ 9 ↦ ℂ n × n https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003580447/ce9022ba-af67-4a01-993e-cfddd27c6ae0/content/eq126.tif"/> . The mappings ρ and α are given by the formulas https://www.w3.org/1998/Math/MathML" display="block"> ρ ( z ) : = max { | λ | : λ ∈ Σ ( z ) } , https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003580447/ce9022ba-af67-4a01-993e-cfddd27c6ae0/content/eq127.tif"/>

  PublisherDOI

• An experimental comparison of methods for computing the numerical radius

  Results in Applied Mathematics · 2024-01-30 · 1 citations

  articleOpen accessSenior authorCorresponding

  We make an experimental comparison of methods for computing the numerical radius of an n×n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in n2+1 real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.

  PublisherDOI

• On the Choice of Sign Defining Householder Transformations

  arXiv (Cornell University) · 2023-08-07

  preprintOpen access1st authorCorresponding

  It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the "wrong" choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.

  PublisherOA PDFDOI

• On the choice of sign defining Householder transformations

  Numerical Algebra Control and Optimization · 2023-12-18 · 1 citations

  articleOpen access1st authorCorresponding

  It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the 'wrong' choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.

  PublisherOA PDFDOI

• An Experimental Comparison of Methods for Computing the Numerical Radius

  arXiv (Cornell University) · 2023-10-07

  preprintOpen accessSenior author

  This software contains MATLAB code to replicate all the experiments and create the associated plots in the following paper (to appear in Results in Applied Mathematics): Tim Mitchell and Michael L. Overton, An Experimental Comparison of Methods for Computing the Numerical Radius.

  PublisherOA PDFDOI

• Multifidelity Robust Controller Design with Gradient Sampling

  SIAM Journal on Scientific Computing · 2023-04-28 · 3 citations

  article

  Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In this work, we introduce multi-fidelity variants of gradient sampling that leverage low-cost, low-fidelity models with low-dimensional state spaces for speeding up the optimization process while nonetheless providing convergence guarantees for a high-fidelity model of the system of interest, which is primarily accessed in the last phase of the optimization process. Our first multi-fidelity method initiates gradient sampling on higher fidelity models with starting points obtained from cheaper, lower fidelity models. Our second multi-fidelity method relies on ensembles of gradients that are computed from low- and high-fidelity models. Numerical experiments with controlling the cooling of a steel rail profile and laminar flow in a cylinder wake demonstrate that our new multi-fidelity gradient sampling methods achieve up to two orders of magnitude speedup compared to the single-fidelity gradient sampling method that relies on the high-fidelity model alone.

  PublisherDOI

• On properties of univariate max functions at local maximizers

  Optimization Letters · 2022-03-28 · 2 citations

  articleOpen accessSenior author

  Abstract More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously differentiable, with Lipschitz second derivative, at all local maximizers, a property that is useful in several applications that we describe. We also investigate whether this smoothness property extends to max functions more generally. We show that the pointwise maximum of a finite set of q -times continuously differentiable univariate functions must have zero derivative at a maximizer for $$q=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , but arbitrarily close to the maximizer, the derivative may not be defined, even when $$q=3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and the maximizer is isolated.

  PublisherOA PDFDOI

• Multi-fidelity robust controller design with gradient sampling

  arXiv (Cornell University) · 2022-05-30

  preprintOpen access

  Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In this work, we introduce multi-fidelity variants of gradient sampling that leverage low-cost, low-fidelity models with low-dimensional state spaces for speeding up the optimization process while nonetheless providing convergence guarantees for a high-fidelity model of the system of interest, which is primarily accessed in the last phase of the optimization process. Our first multi-fidelity method initiates gradient sampling on higher fidelity models with starting points obtained from cheaper, lower fidelity models. Our second multi-fidelity method relies on ensembles of gradients that are computed from low- and high-fidelity models. Numerical experiments with controlling the cooling of a steel rail profile and laminar flow in a cylinder wake demonstrate that our new multi-fidelity gradient sampling methods achieve up to two orders of magnitude speedup compared to the single-fidelity gradient sampling method that relies on the high-fidelity model alone.

  PublisherOA PDFDOI

• Behavior of Limited Memory BFGS When Applied to Nonsmooth Functions and Their Nesterov Smoothings

  Springer proceedings in mathematics & statistics · 2021-01-01 · 5 citations

  book-chapterSenior author
  PublisherDOI

Recent grants

• Nonsmooth, Nonconvex Optimization: Algorithms, Theory, and Applications

  NSF · $496k · 2007–2010

• Optimization of Pseudospectra

  NSF · $384k · 2004–2007

• Scalable Methods for Approximating and Optimizing Robust Stability Functions

  NSF · $650k · 2010–2014

• Spectral Value Sets: Theory, Algorithms and Applications

  NSF · $432k · 2013–2016

• Robust Stability of Linear Dynamical Systems: Algorithms, Theory and Applications

  NSF · $350k · 2016–2020

Frequent coauthors

• James V. Burke

  43 shared

• Adrian S. Lewis

  Cornell University

  38 shared

• Didier Henrion

  Laboratoire d'Analyse et d'Architecture des Systèmes

  26 shared

• Tim Mitchell

  Queens College, CUNY

  25 shared

• Mert Gürbüzbalaban

  Rutgers, The State University of New Jersey

  23 shared

• A Nasrollah Zadeh Asl

  University of Chicago

  18 shared

• Tamar Schlick

  New York University

  15 shared

• Marc Millstone

  IBM (United States)

  15 shared

Labs

• Michael Overton's LabPI

  Not provided

Education

• B.S., Computer Science

  University of British Columbia

  1974

• M.S., Computer Science

  Stanford University

  1977

• Ph.D., Computer Science

  Stanford University

  1979

Awards & honors

• Fellow of SIAM
• Fellow of IMA
• IEEE Senior Fellow