David Shanno

April 20, 1938

Brief Biography

Shanno Fellow Portrait

David Shanno has made significant contributions to optimization and mathematical programming in computer science. Shanno studied mathematics and philosophy from Yale University. At the graduate level, he studied mathematics at Carnegie-Mellon University, receiving a PhD in mathematics under the supervision of Gerald L. Thompson. Shanno taught at the University of Chicago, the University of Arizona, and the University of California, Davis, before joining the faculty at the Rutgers Center for Operations Research (RUTCOR).  

In 1970, he was one of the developers of the BFGS algorithm (Broyden-Fletcher-Goldfarb-Shanno) with Donald Goldfarb, Charles George Broyden, and Roger Fletcher. The algorithm approximate Isaac Newton’s method in optimization and is implemented in various software languages to solve unconstrained nonlinear optimization problems. In the 1990s and early 2000s, Shanno published a series of papers on interior point methods for linear and nonlinear programming. A significant paper he co-authored with Robert J. Vanderbei in 2000 showed that unlike linear and convex quadratic programming, higher order corrections are not useful for nonconvex nonlinear programing, though a variant of existing algorithms can improve performance.

Shanno was an associate editor of Mathematical Programming in the 1980s. His other editorial positions include departmental editor of the management science and operations research section of Communications of the Association of Computing Machinery (1973-1980) and associate editor of the Journal of Optimization Theory and Applications (1982-1990).

In 1991, the Mathematical Programming Society awarded Shanno, Roy Marsten, and Irvin Lustig the Beale-Orhcard-Hays Prize for Excellence in Computational Mathematical Programming. The following year, the trio, along with Nimrod Megiddo, Akiko Yoshise, Toshihto Noma, and Masakazu Kojima, received the Operations Research Society of America’s (ORSA) Computer Science Technical Section Prize for research excellence in the interface between operations research and computer science. In 2005, Shanno was elected a Fellow of ORSA’s successor, the Institute for Operations Research and the Management Sciences. 

Other Biographies

Wikipedia (Deutsche) Entry for David Shanno


Yale University, BA 1959

Carnegie-Mellon University, MS 1962

Carnegie-Mellon University, PhD 1967 (Mathematics Genealogy)


Academic Affiliations

Key Interests in OR/MS


Oral Histories

David Shanno (2017). Interview by Irv Lustig, December 14, 2017, Washington Crossing, PA.

NOTE:  The video chapter transcripts below are searchable, with search results displayed as marks on the time bar above the search box.  Click a mark to jump to the search word or phrase in the video and transcript, or click on any word in the transcript to jump to that point in the video.

Jump to Chapters

Chapter 1: Early Life
Chapter 2: College at Yale
Chapter 3: First Job at Union Carbide
Chapter 4: Graduate Work at Carnegie Mellon
Chapter 5: From Gulf Oil to Academia
Chapter 6: The BFGS Algorithm
Chapter 7: From Unconstrained to Constrained Optimization
Chapter 8: Interior Point Methods for Linear Programming
Chapter 9: Interior Point Methods for Nonlinear Programming
Chapter 10: Career Retrospective
Chapter 11: Perspectives on the Field of Operations Research
Chapter 12: Current Activities
Chapter 13: Concluding Remarks

Memoirs and Autobiographies


Rutgers Center for Operations Research. David Shanno: Curriculum Vitae. Accessed May 5, 2015. (link

Awards and Honors

E.M.L. Beale - W. B. Orchard-Hayes Prize for Excellence in Computational Mathematical Programming 1991

INFORMS Computing Society Prize 1992

Institute for Operations Research and the Management Sciences Fellow 2005

Selected Publications

Shanno D. F. (1970) Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation, 24(111): 647-656.

Phua K. H. & Shanno D. F. (1978) Matrix conditioning and nonlinear optimization. Mathematical Programming, 14(1): 149-160.

Shanno D. F. (1978) Conjugate gradient methods with inexact searches. Mathematics of Operations Research, 3(3): 244-256.

Shanno D. F. (1978) On the convergence of a new conjugate gradient algorithm. SIAM Journal on Numerical Analysis, 15(6): 1247-1257.

Phua K. H. & Shanno D. F. (1980) Remark on ‘Algorithm 500: minimization of unconstrained multivariate functions [e4]’. ACM Transactions on Mathematical Software (TOMS), 6(4): 618-622.

Shanno D. F. (1985) On broyden-goldfarb-shanno method. Journal of Optimization Theory and Applications, 46(1): 87-94.

Lustig I. J., Marsten R. E., Shanno D. F. (1994) Interior point methods for linear programming: computational state of the art. ORSA Journal on Computing, 6(1): 1-14.

Shanno D. F. & Vanderbei R. J. (1999) An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications, 13(1-3): 231-252.

Shanno D. F. & Vanderbei R. J. (2000) Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods. Mathematical Programming, 87(2): 303-316.

Benson H. Y., Shanno D. F., & Vanderbei R. J. (2002) Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions. Computations Optimization and Applications, 23(2): 257-272.

Shanno, D (2012) Who Invented the Interior-Point Method? In Grötschel, M. ed. Documenta MathematicaExtra Volume "Optimization Stories" 55-64. (link)