Alan J. Hoffman

Born:
May 30, 1924

Brief Biography

Alan Hoffman was born and raised in New York City and entered Columbia University on a Pulitzer scholarship in 1940, intending to become a mathematics professor. He served in the U.S. Army 1943-46, most notably with the 3186th Signal Service Battalion in Europe (England, France, Germany) and the Pacific (Philippine Islands, Japan). Returning to Columbia, he received his A.B. degree in 1947 and PhD. in 1950, with a thesis on the foundations of inversion geometry. After a year at the Institute for Advanced Study, he joined the Mathematical Sciences department of the National Bureau of Standards (now the National Institute of Standards and Technology) in Washington, where he became the leader of the Bureau's research in a new subject: linear programming. Among the accomplishments of Hoffman and his colleagues: (1) experiments showing simplex method superior to its contemporary competitors; (2) concept of totally unimodular matrices;(3) Lipschitz conditions for systems of linear inequalities;  (4) bounds on eigenvalues of normal matrices; (5) properties of smooth patterns of production.  In 1956, he left the Bureau to become a Scientific Liason Officer (mathematics) at the Office of Naval Resarch in London, returning the next year to join Management and Consultation Services of General Company in New York. In 1961, he joined the IBM company at the Watson Research ,Center in Yorktown Heights, New York, retiring in 2002 as IBM Fellow Emeritus. Over the course of his career he published over one hundred and sixty academic papers. 

As a member of the Mathematical Sciences Department, he worked closely with Ralph Gomory and began a career spanning over four decades. Hoffman played a significant role in the hiring of other individuals, particularly his close friend and longtime collaborator, Philip S. Wolfe. Though quite active at IBM, Hoffman found the time to be an adjunct professor, teaching at City University of New York, Yale University, Stanford, and Princeton. Over twenty one years, he supervised fifteen different PhD students at four different institutions. 

Hoffman served on the editorial board of eleven different journals including Linear Algebra and its Applications which he helped establish in 1968. In 1971-1972, Hoffman served as the director of the Business Analytics and Mathematical Sciences (BAMS) Department at IBM. BAMS conducted active research in such fields as optimization, simulation, and algorithms.

In 1992, Hoffman was awarded the John von Neumann Prize with Wolfe by ORSA and TIMS. He and Wolfe were recognized as the intellectual leaders of mathematical programming. Hoffman was cited for his work in combinatorics and linear programming. His early work in determining the computational efficiency of the simplex method during his time at the NBS was also lauded.

Other Biographies

Wikipedia Entry for Alan Hoffman (mathematician)

Rothblum U. G. (1989) Preface. Linear Algebra and its Applications, Special Issue Dedicated to Alan J. Hoffman, 144-115: 1-16. 

Education

Columbia University, A.B. 1947 

Columbia University, PhD 1950 (Mathematics Genealogy

Affiliations

Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS

Methodologies

Oral Histories

Alan Hoffman Interview by Irv Lustig May 4, 2001. Video by Irv Lustig, Short Hills, NJ.

NOTE: The video chapter transcripts 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: First Job at National Bureau of Standards  
   
Chapter 2: Cycling and the Simplex Method  
   
Chapter 3: Evolution of the Hoffman-Wielandt Theorem  
   
Chapter 4: Duality and the König-Egerváry Theorem  
   
Chapter 5: Computational Comparisons with the Simplex Method  
   
Chapter 6: An Early Combinatorial Auction  
   
Chapter 7: Solving Linear Programs on SEAC  
   
Chapter 8: Explaining Optimization  
   
Chapter 9: A Historical Perspective  
   
Chapter 10: Looking Forward  
   
Chapter 11: The Growth of Optimization  
   
Chapter 12: Criticism of Optimization  
   
Chapter 13: Concluding Remarks  

Jump to Chapters

Chapter 1: First Job at National Bureau of Standard
Chapter 2: Cycling and the Simplex Method
Chapter 3: Evolution of the Hoffman-Wielandt Theorem
Chapter 4: Duality and the König-Egerváry Theorem
Chapter 5: Computational Comparisons with the Simplex Method
Chapter 6: An Early Combinatorial Auction
Chapter 7: Solving Linear Programs on SEAC
Chapter 8: Explaining Optimization
Chapter 9: A Historical Perspective
Chapter 10: Looking Forward
Chapter 11: The Growth Of Optimization
Chapter 12: Criticism of Optimization
Chapter 13: Concluding Remarks

Memoirs and Autobiographies

Memoirs

Hoffman A. J. (1991) Linear Programming at the National Bureau of Standards. Lenstra J. K., Rinooy-Kan A., & Schrijver A. in History of Mathematical Programming, a collection of personal reminiscences, 62-64. Elsevie Science Publishers: New York. 

Awards and Honors

National Academy of Science 1982

John von Neumann Theory Prize 1992  

Founder's Award, Mathematical Programming Society 2000  

The Institute for Operations Research and the Management Sciences Fellow 2002

Selected Publications

Hoffman A. J. (1953) Cycling in the simplex algorithm, Technical report 2974. National Bureau of Standards.

Hoffman A. J. & Jacobs W. (1954) Smooth patterns of production. Management Science, 1(1): 86-91.

Hoffman A. J. & Kruskal J. B. (1956) Integral Boundary Pointss of Convex Polyhedra. Kuhn H. W. & Tucker A. J., eds. Linear Inequalities and Related Systems, 223-246. Princeton University Press: Princeton.  

Hoffman A. J. (1960) Some recent applications of the theory of linear inequalities to extremal combinatorial analysis. Combinatorial Analysis: Proceedings of the Tenth Symposium in Applied Mathematics, 113-127.

Gilmore P. C. & Hoffman A. J. (1962) A characterization of comparability graphs and of interval graphs, No. RC-651. IBM Watson Research Center: Yorktown Heights, New York.

Gomory R. & Hoffman A. J. (1963) On the convergence of an integer-programming process. Naval Research Logistics Quarterly, 10(1): 369-373.

Hoffman A. J. (1963) On abstract dual linear programs. Naval Research Logistics Quarterly, 10(1): 369-373.

Barnes E. R. & Hoffman A. J. (1984) Partitioning, spectra, and linear programming. Progress in Combinatorial Optimization, 13-25. Wiley: New York.

Hoffman A. J. & Wolfe P. (1985) History. Lawler E. L., Lenstra J. K., Rimmooy Kan A. H. G., & Shmoys D. B., eds. The Traveling Salesman Problem. John Wiley & Sons: New York. 

Additional Resources

World Scientific. (2003) Selected Papers from Alan J. Hoffman with Commentary. Accessed July 12, 2018. (link)