Jorge Nocedal

Last updated

Jorge Nocedal (born 1952) is an applied mathematician, computer scientist and the Walter P. Murphy professor at Northwestern University who in 2017 received the John Von Neumann Theory Prize. He was elected a member of the National Academy of Engineering in 2020.

Contents

Nocedal specializes in nonlinear optimization, both in the deterministic and stochastic setting. The motivation for his current algorithmic and theoretical research stems from applications in image and speech recognition, recommendation systems, and search engines. [1] In the past, he has also worked on equilibrium problems with application in robotics, traffics, and games, optimization applications in finance, as well as PDE-constrained optimization. [2]

Biography

Nocedal was born and raised in Mexico. He obtained a B.Sc. in physics from the National University of Mexico in 1974. From 1974 to 1978, Nocedal studied at Rice University where he obtained a PhD in mathematical sciences under the supervision of Richard A. Tapia. Prior to joining Northwestern University in 1983, Nocedal spent three years (1978-1981) as an assistant professor at the National University of Mexico and two years (1981-1983) as a research assistant at the Courant Institute of Mathematical Sciences at NYU. Nocedal joined the Electrical Engineering and Computer Sciences department at Northwestern University in 1983. He held this appointment until 2012, before joining the Industrial Engineering and Management Sciences department, where he served as the David and Karen Sachs Professor and Chair from 2013 to 2017. [3]

Contributions

Nocedal is well-known for his research in nonlinear optimization, particularly for his work on L-BFGS [4] [5] and his textbook Numerical Optimization. [6]

In 2001, Nocedal co-founded Ziena Optimization Inc. and co-developed the KNITRO software package. [7] Nocedal was a chief scientist at Ziena Optimization Inc. from 2002 to 2012 before the company was subsequently bought by Artelys in 2015. [3] [8]

Awards and honors

Nocedal has won numerous awards in the fields of nonlinear optimization, applied mathematics and operations research. In 1998, he was the invited speaker to the International Congress of Mathematicians in Berlin. [9] [10] He was named an ISI Highly Cited Researcher in 2004. He received the George B. Dantzig Prize in 2012 [11] and the Charles Broyden Prize in 2009. [12] He was also named a SIAM Fellow in 2010. [13] In 2017, he received the INFORMS John Von Neumann Theory Prize. [14] Nocedal was elected a member of the National Academy of Engineering in 2020 for contributions to the theory, design, and implementation of optimization algorithms and machine learning software. [15]

Related Research Articles

<span class="mw-page-title-main">George Dantzig</span> American mathematician (1914-2005)

George Bernard Dantzig was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.

The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual who has made fundamental and sustained contributions to theory in operations research and the management sciences.

In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually improving an approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations via a generalized secant method.

<span class="mw-page-title-main">Éva Tardos</span> Hungarian mathematician

Éva Tardos is a Hungarian mathematician and the Jacob Gould Schurman Professor of Computer Science at Cornell University.

Limited-memory BFGS is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) using a limited amount of computer memory. It is a popular algorithm for parameter estimation in machine learning. The algorithm's target problem is to minimize over unconstrained values of the real-vector where is a differentiable scalar function.

<span class="mw-page-title-main">Michael J. D. Powell</span>

Michael James David Powell was a British mathematician, who worked in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

<span class="mw-page-title-main">Dimitri Bertsekas</span>

Dimitri Panteli Bertsekas is an applied mathematician, electrical engineer, and computer scientist, a McAfee Professor at the Department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, and also a Fulton Professor of Computational Decision Making at Arizona State University, Tempe.

Ellis Lane Johnson is the Professor Emeritus and the Coca-Cola Chaired Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology in Atlanta, Georgia.

Yinyu Ye is a Chinese American theoretical computer scientist working on mathematical optimization. He is a specialist in interior point methods, especially in convex minimization and linear programming. He is a professor of Management Science and Engineering and Kwoh-Ting Li Chair Professor of Engineering at Stanford University. He also holds a courtesy appointment in the Department of Electrical Engineering. Ye also is a co-founder of minMax Optimization Inc.

Roger Jean-Baptiste Robert Wets is a "pioneer" in stochastic programming and a leader in variational analysis who publishes as Roger J-B Wets. His research, expositions, graduate students, and his collaboration with R. Tyrrell Rockafellar have had a profound influence on optimization theory, computations, and applications. Since 2009, Wets has been a distinguished research professor at the mathematics department of the University of California, Davis.

<span class="mw-page-title-main">R. Tyrrell Rockafellar</span> American mathematician

Ralph Tyrrell Rockafellar is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics. He is the author of four major books including the landmark text "Convex Analysis" (1970), which has been cited more than 27,000 times according to Google Scholar and remains the standard reference on the subject, and "Variational Analysis" for which the authors received the Frederick W. Lanchester Prize from the Institute for Operations Research and the Management Sciences (INFORMS).

Charles George Broyden was a mathematician who specialized in optimization problems and numerical linear algebra. While a physicist working at English Electric Company from 1961–1965, he adapted the Davidon–Fletcher–Powell formula to solving some nonlinear systems of equations that he was working with, leading to his widely cited 1965 paper, "A class of methods for solving nonlinear simultaneous equations". He was a lecturer at UCW Aberystwyth from 1965–1967. He later became a senior lecturer at University of Essex from 1967–1970, where he independently discovered the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The BFGS method has then become a key technique in solving nonlinear optimization problems. Moreover, he was among those who derived the symmetric rank-one updating formula, and his name was also attributed to Broyden's methods and Broyden family of quasi-Newton methods. After leaving the University of Essex, he continued his research career in the Netherlands and Italy, being awarded the chair at University of Bologna. In later years, he began focusing on numerical linear algebra, in particular conjugate gradient methods and their taxonomy.

Arkadi Nemirovski is a professor at the H. Milton Stewart School of Industrial and Systems Engineering at the Georgia Institute of Technology. He has been a leader in continuous optimization and is best known for his work on the ellipsoid method, modern interior-point methods and robust optimization.

<span class="mw-page-title-main">Yurii Nesterov</span> Russian mathematician

Yurii Nesterov is a Russian mathematician, an internationally recognized expert in convex optimization, especially in the development of efficient algorithms and numerical optimization analysis. He is currently a professor at the University of Louvain (UCLouvain).

The Truncated Newton Method originated in a paper by Ron Dembo and Trond Steihaug first published in Mathematical Programming '. Convergence results for this algorithm can be found in: Dembo, Ron S., Stanley C. Eisenstat, and Trond Steihaug. "Inexact newton methods." SIAM Journal on Numerical analysis 19.2 (1982): 400-408. Also known as Hessian-free optimization, are a family of optimization algorithms designed for optimizing non-linear functions with large numbers of independent variables. A truncated Newton method consists of repeated application of an iterative optimization algorithm to approximately solve Newton's equations, to determine an update to the function's parameters. The inner solver is truncated, i.e., run for only a limited number of iterations. It follows that, for truncated Newton methods to work, the inner solver needs to produce a good approximation in a finite number of iterations; conjugate gradient has been suggested and evaluated as a candidate inner loop. Another prerequisite is good preconditioning for the inner algorithm.

<span class="mw-page-title-main">Gérard Cornuéjols</span> American mathematician

Gérard Pierre Cornuéjols is the IBM University Professor of Operations Research in the Carnegie Mellon University Tepper School of Business. His research interests include facility location, integer programming, balanced matrices, and perfect graphs.

Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.

Donald Goldfarb is an American mathematician, best known for his works in mathematical optimization and numerical analysis.

The Dantzig Prize is given every 3 years to one or more individuals for research which, by virtue of its originality, breadth, and depth, has a major impact on the field of mathematical programming. It is named in honor of George B. Dantzig and is awarded jointly by the Society for Industrial and Applied Mathematics (SIAM) and the Mathematical Optimization Society (MOS). The prize fund was established in 1979, and the prize first awarded in 1982.

<span class="mw-page-title-main">Richard W. Cottle</span>

Richard W. Cottle is an American mathematician. He was a professor of Management Science and Engineering at Stanford University, starting as an Acting Assistant Professor of Industrial Engineering in 1966 and retiring in 2005. He is notable for his work on mathematical programming/optimization, “Nonlinear programs”, the proposal of the linear complementarity problem, and the general field of operations research.

References

  1. ↑ "Jorge Nocedal, Walter P. Murphy Professor". Industrial Engineering & Management Sciences. Northwestern University. Retrieved 2017-12-04.
  2. ↑ "Jorge Nocedal, Walter P. Murphy Professor: Research Interests". Industrial Engineering & Management Sciences. Northwestern University. Retrieved 2017-12-04.
  3. 1 2 Nocedal, Jorge. "Jorge Nocedal CV" (PDF). Retrieved December 3, 2017.
  4. ↑ Liu, Dong C.; Nocedal, Jorge (1989-08-01). "On the limited memory BFGS method for large scale optimization". Mathematical Programming. 45 (1–3): 503–528. CiteSeerX   10.1.1.110.6443 . doi:10.1007/BF01589116. ISSN   0025-5610. S2CID   5681609.
  5. ↑ Byrd, R.; Lu, P.; Nocedal, J.; Zhu, C. (1995-09-01). "A Limited Memory Algorithm for Bound Constrained Optimization". SIAM Journal on Scientific Computing. 16 (5): 1190–1208. CiteSeerX   10.1.1.15.6761 . doi:10.1137/0916069. ISSN   1064-8275.
  6. ↑ Numerical Optimization | Jorge Nocedal. Springer. Springer Series in Operations Research and Financial Engineering. Springer. 2006. ISBN   9780387303031.
  7. ↑ Byrd, Richard H.; Nocedal, Jorge; Waltz, Richard A. (2006). Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications. Springer, Boston, MA. pp. 35–59. CiteSeerX   10.1.1.154.4900 . doi:10.1007/0-387-30065-1_4. ISBN   9780387300634.
  8. ↑ "Artelys | Optimization solutions - Artelys Knitro - Nonlinear optimization solver". www.artelys.com. Retrieved 2017-12-04.
  9. ↑ "International Mathematical Union (IMU)". www.mathunion.org.
  10. ↑ Byrd, Richard H.; Nocedal, Jorge (1998). "Active set and interior methods for nonlinear optimization". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III. pp. 667–676.
  11. ↑ "SIAM: The George B. Dantzig Prize". www.siam.org.
  12. ↑ "Charles Broyden Prize". Taylor & Francis.
  13. ↑ "SIAM Fellows". fellows.siam.org.
  14. ↑ INFORMS. "John von Neumann Theory Prize". INFORMS.
  15. ↑ "National Academy of Engineering Elects 87 Members and 18 International Members". National Academy of Engineering. February 6, 2020.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.