Jorge Nocedal (born 1950) 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.
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]
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]
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]
Nocedal has won numerous awards in the fields of nonlinear optimization, applied mathematics and operations research. In 1998, he was an 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]
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.
Richard Alfred Tapia is an American mathematician and University Professor at Rice University in Houston, Texas, the university's highest academic title. In 2011, President Obama awarded Tapia the National Medal of Science. He is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University.
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.
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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).
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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.
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).
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