Jorge Nocedal

About

My research focuses on the creation of new algorithms for solving complex optimization problems. Over the years, this research has been motivated by applications as diverse as weather forecasting, engineering design and machine learning. There are always new challenges as scientist and engineers create models of increasing nonlinearity and dimensionality, amid uncertainty. To test the power of our algorithms and to make them widely available, my group has developed several software packages (some open source and some commercial) that are used in a wide range of applications. They include L-BFGS, KNITRO and L-BFGS-B. My view is that theory, algorithm design, and software are equally important in the creation of new algorithms. This is reflected in the textbook “Numerical Optimization”, which I co-authored with Steve Wright.

Research topics

• Computer Science
• Mathematical optimization
• Mathematics
• Applied mathematics
• Algorithm

Selected publications

• An investigation of Newton-Sketch and subsampled Newton methods

  Optimization methods & software · 2020-02-12 · 33 citations

  preprintOpen accessSenior authorCorresponding

  Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. We study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not bee…

  PublisherOA PDFDOI

• On the numerical performance of finite-difference-based methods for derivative-free optimization

  Optimization methods & software · 2022-09-26 · 28 citations

  articleSenior author
  PublisherDOI

• A trust region method for noisy unconstrained optimization

  Mathematical Programming · 2023-03-24 · 24 citations

  articleSenior authorCorresponding
  PublisherDOI

• Adaptive Finite-Difference Interval Estimation for Noisy Derivative-Free Optimization

  SIAM Journal on Scientific Computing · 2022-08-01 · 15 citations

  articleSenior author

  A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is noisy, the optimal choice requires information about the noise level and higher-order derivatives of the function, which is often unavailable. Given the noise level of the function, we propose a bisection search for finding a finite-difference interval for any f…

  PublisherDOI

• Constrained and composite optimization via adaptive sampling methods

  IMA Journal of Numerical Analysis · 2023-05-12 · 13 citations

  articleOpen accessSenior author

  Abstract The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems, in which the objective function is stochastic and the constraints are deterministic. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min $f(x) + h(x)$, where $f$ is stochastic and $h$ is convex (but not necessarily differentiable). Adaptive sampling methods employ a mechani…

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Market-Based Calibration of Pricing Models for Financial and Energy Option Contracts

  NSF · $160k · 2010–2013

• Nonlinear Optimization: Algorithms, Theory and Software

  NSF · $291k · 2008–2012

• Active-Set and Interior Algorithms for Non-Linear Optimization

  NSF · $250k · 2005–2009

Frequent coauthors

• Richard H. Byrd

  University of Colorado Boulder

  43 shared

• Richard Byrd

  University of Colorado Boulder

  18 shared

• José Luis Morales

  Instituto Politécnico Nacional

  15 shared

• Richard A. Waltz

  University of Southern California

  14 shared

• Figen Öztoprak

  Gebze Technical University

  14 shared

• Raghu Bollapragada

  13 shared

• Hao-Jun Michael Shi

  10 shared

• Frank E. Curtis

  Lehigh University

  9 shared

Labs

• Northwestern UniversityPI

Education

• B.S.

  UNAM, Mexico

• Ph.D.

  Rice University

Awards & honors

• 2012 George B. Dantzig Prize
• 2017 Von Neumann Theory Prize

Similar researchers at Northwestern University

• Tobin J. Marksh-176
• Joseph Hupph-171
• James D Thomash-160