Herbert Eli "Herb" Scarf was an American mathematical economist and Sterling Professor of Economics at Yale University. Scarf was born in Philadelphia, the son of Jewish emigrants from Ukraine and Russia and Louis Scarf, he was a member of the American Academy of Sciences. During his undergraduate work he finished in the top 10 of the 1950 William Lowell Putnam Mathematical Competition, the major mathematics competition between universities across the United States and Canada, he received his PhD from Princeton in 1954. Among his notable works is a seminal paper in cooperative game in which he showed sufficiency for a core in general balanced games. Sufficiency and necessity had been shown by Lloyd Shapley for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization. Scarf received the 1973 Frederick W. Lanchester Award for his contribution The Computation of Economic Equilibria with the collaboration of Terje Hansen, which pioneered the use of numeric algorithms to solve general equilibrium systems using Applied general equilibrium models.
Personal web site The works of Herbert Scarf Herbert Scarf at Find a Grave
Michel Louis Balinski was an applied mathematician, operations research analyst and political scientist. As an American, educated in the United States, he lived and worked in the United States and France, he was known for his work in optimization, convex polyhedra, stable matching, the theory and practice of electoral systems, jury decision, social choice. He was Directeur de Recherche de classe exceptionnelle of the C. N. R. S. at the Ecole Polytechnique. He was awarded the John von Neumann Theory Prize by INFORMS in 2013. Michel Balinski was born in Geneva, the grandson of the Polish bacteriologist and founder of UNICEF, Ludwik Rajchman. Brought up by his mother Irena Balinska and his grandparents, they were living in France when the Nazis invaded in 1940, they fled via Portugal to the United States. He graduated from the Edgewood School in Greenwich CT in 1950, earned a B. A. degree cum laude in mathematics at Williams College in 1954 and a M. Sc. in economics at the Massachusetts Institute of Technology in 1956.
He completed a Ph. D. in mathematics at Princeton University in 1959 under the supervision of Albert W. Tucker. After completing his Ph. D. Balinski remained at Princeton University as a Research Associate Lecturer in mathematics. From 1963 to 1965 he was Associate Professor of Economics at the Wharton School of the University of Pennsylvania, he was appointed to the Graduate School of the City University of New York, first as Associate Professor Professor of Mathematics. One of his doctoral students at the City University was another noted mathematician, Louis Billera, through whom he has many academic descendants. In 1978 he was appointed Professor of Organization and Management and of Administrative Sciences at Yale. In parallel with his academic work Balinski engaged in consulting as of the time he was a graduate student at Princeton. A participant in the beginnings of what became the consulting firm Mathematica, he was a Senior Consultant with the firm from 1962 to 1974, he acted as a consultant elsewhere, including the Rand Corporation, Mobil Oil Research, the ORTF, the Mayor's office of the City of New York, Econ, Inc.
From 1975 to 1977 he was Chairman of System and Decision Sciences at IIASA at Laxenburg, Austria. In 1980 Michel Balinski settled in France, becoming Directeur de Recherche de classe exceptionnelle of the CNRS at the Laboratoire d’Econométrie of the Ecole Polytechnique in 1983. Concurrently he was Leading Professor of Applied Mathematics and Statistics and of Economics at SUNY Stony Brook, where he founded and was the first Director of the Institute for Decision Sciences. Upon becoming Director of the Laboratoire d’Econométrie he co-founded and co-directed the joint Ecole Polytechnique/Université de Paris 1 masters program "Modélisation et méthodes mathématiques en économie: optimisation et analyse stratégiques," and its successor the joint Ecole Polytechnique/Université Pierre et Marie Curie masters program "Optimisation, jeux et modélisation en économie." He was a visiting professor at other institutions, including the Ecole Polytechnique Fédérale de Lausanne, the Université Scientifique et Médicale de Grenoble, the Universidad de Chile in Santiago, INSEAD in Fontainebleau.
Balinski was the founding Editor-in-Chief of the journal Mathematical Programming in 1971, one of the founders of the Mathematical Optimization Society in 1970, President of that society from 1986 to 1989. Balinski's Ph. D. thesis concerned the vertex enumeration problem, the algorithmic problem of listing all vertices of a convex polytope or finding all optimal solutions of a linear program, some of his subsequent work continued to concern polyhedral combinatorics. The thesis includes the fundamental theorem, published in 1961, that the skeletons of polytopes in "n"-space viewed as graphs are "n"-connected, meaning that at least "n" edges must be removed to disconnect the graph of the remaining vertices and edges, he proved the Hirsch conjecture for several different classes of polytopes associated with the transportation problem, showed that the diameter of the skeleton of the assignment polytope viewed as a graph is 2, found the polytope whose vertices are the stable matchings of the university admissions problem.
His contributions to linear and nonlinear optimization include a primal/dual simplex method that incorporates a natural proof of termination and leads to a self-contained, elementary but rigorous, constructive account of the theory and the basic computational tool of linear programming. His work in integer programming includes the formulation and analysis of the fixed cost transportation problem. Together with Mourad Baïou, he developed a new formulation of stable matchings and generalizations in terms of graphs, providing a unified notation and tool leading to new proofs of known results and new results.
George Bernard Dantzig was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science and statistics. Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, for his other work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture by Jerzy Neyman. Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford. Born in Portland, George Bernard Dantzig was named after George Bernard Shaw, the Irish writer, his father, Tobias Dantzig, was a mathematician and linguist, his mother, Anja Dantzig, was a linguist of French Jewish origin. Dantzig's parents met during their study at the University of Paris, where Tobias studied mathematics under Henri Poincaré, after whom Dantzig's brother was named.
The Dantzigs immigrated to the United States, where they settled in Oregon. Early in the 1920s the Dantzig family moved from Baltimore to Washington, his mother became a linguist at the Library of Congress, his father became a math tutor at the University of Maryland, College Park. Dantzig attended Central High School. By the time he reached high school he was fascinated by geometry, this interest was further nurtured by his father, challenging him with complicated problems in projective geometry. George Dantzig received his B. S. from University of Maryland in 1936 in mathematics and physics, part of the University of Maryland College of Computer and Natural Sciences. He earned his master's degree in mathematics from the University of Michigan in 1938. After a two-year period at the Bureau of Labor Statistics, he enrolled in the doctoral program in mathematics at the University of California, where he studied statistics under Jerzy Neyman. With the outbreak of World War II, Dantzig took a leave of absence from the doctoral program at Berkeley to join the U.
S. Air Force Office of Statistical Control. In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph. D. that year. Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the comptroller. In 1952 Dantzig joined the mathematics division of the RAND Corporation. By 1960 he became a professor in the Department of Industrial Engineering at UC Berkeley, where he founded and directed the Operations Research Center. In 1966 he joined the Stanford faculty of Computer Science. A year the Program in Operations Research became a full-fledged department. In 1973 he founded the Systems Optimization Laboratory there. On a sabbatical leave that year, he headed the Methodology Group at the International Institute for Applied Systems Analysis in Laxenburg, Austria, he became the C. A. Criley Professor of Transportation Sciences at Stanford, kept going, well beyond his mandatory retirement in 1985, he was a member of the National Academy of Sciences, the National Academy of Engineering, the American Academy of Arts and Sciences.
Dantzig was the recipient of many honors, including the first John von Neumann Theory Prize in 1974, the National Medal of Science in 1975, an honorary doctorate from the University of Maryland, College Park in 1976. The Mathematical Programming Society honored Dantzig by creating the George B. Dantzig Prize, bestowed every three years since 1982 on one or two people who have made a significant impact in the field of mathematical programming. Dantzig died on May 13, 2005, in his home in Stanford, California, of complications from diabetes and cardiovascular disease, he was 90 years old. Freund wrote further that "through his research in mathematical theory, economic analysis, applications to industrial problems, Dantzig contributed more than any other researcher to the remarkable development of linear programming". Dantzig's work allows the airline industry, for example, to schedule crews and make fleet assignments. Based on his work tools are developed "that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed.
The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It is used in manufacturing, revenue management, telecommunications, architecture, circuit design and countless other areas". An event in Dantzig's life became the origin of a famous story in 1939, while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard; when Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days he handed in completed solutions for the two problems, still believing that they were an assignment, overdue. Six weeks Dantzig received a visit from an excited professor Neyman, eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics.
He had prepared one of Dantzig's solutions for publication in a mathematical journal. As Dantzig told it in a 1986 interview in the College Mathematics Journal: A year when I began t
Václav Chvátal (Czech: is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Canada. He has published extensively on topics in graph theory and combinatorial optimization. Chvátal was born in Prague in 1946 and educated in mathematics at Charles University in Prague, where he studied under the supervision of Zdeněk Hedrlín, he fled Czechoslovakia in 1968, three days after the Soviet invasion, completed his Ph. D. in Mathematics at the University of Waterloo, under the supervision of Crispin St. J. A. Nash-Williams, in the fall of 1970. Subsequently, he took positions at McGill University, Stanford University, the Université de Montréal, Rutgers University before returning to Montreal for the Canada Research Chair in Combinatorial Optimization at Concordia and the Canada Research Chair in Discrete Mathematics till his retirement. Chvátal first learned of graph theory in 1964, on finding a book by Claude Berge in a Pilsen bookstore and much of his research involves graph theory: His first mathematical publication, at the age of 19, concerned directed graphs that cannot be mapped to themselves by any nontrivial graph homomorphism Another graph-theoretic result of Chvátal was the 1970 construction of the smallest possible triangle-free graph, both 4-chromatic and 4-regular, now known as the Chvátal graph.
A 1972 paper relating Hamiltonian cycles to connectivity and maximum independent set size of a graph, earned Chvátal his Erdős number of 1. If there exists an s such that a given graph is s-vertex-connected and has no -vertex independent set, the graph must be Hamiltonian. Avis et al. tell the story of Chvátal and Erdős working out this result over the course of a long road trip, thanking Louise Guy "for her steady driving." In a 1973 paper, Chvátal introduced the concept of graph toughness, a measure of graph connectivity, connected to the existence of Hamiltonian cycles. A graph is t-tough if, for every k greater than 1, the removal of fewer than tk vertices leaves fewer than k connected components in the remaining subgraph. For instance, in a graph with a Hamiltonian cycle, the removal of any nonempty set of vertices partitions the cycle into at most as many pieces as the number of removed vertices, so Hamiltonian graphs are 1-tough. Chvátal conjectured that 3/2-tough graphs, that 2-tough graphs, are always Hamiltonian.
Some of Chvátal's work concerns families of sets, or equivalently hypergraphs, a subject occurring in his Ph. D. thesis, where he studied Ramsey theory. In a 1972 conjecture that Erdős called "surprising" and "beautiful", that remains open he suggested that, in any family of sets closed under the operation of taking subsets, the largest pairwise-intersecting subfamily may always be found by choosing an element of one of the sets and keeping all sets containing that element. In 1979, he studied a weighted version of the set cover problem, proved that a greedy algorithm provides good approximations to the optimal solution, generalizing previous unweighted results by David S. Johnson and László Lovász. Chvátal first became interested in linear programming through the influence of Jack Edmonds while Chvátal was a student at Waterloo, he recognized the importance of cutting planes for attacking combinatorial optimization problems such as computing maximum independent sets and, in particular, introduced the notion of a cutting-plane proof.
At Stanford in the 1970s, he began writing his popular textbook, Linear Programming, published in 1983. Cutting planes lie at the heart of the branch and cut method used by efficient solvers for the traveling salesman problem. Between 1988 and 2005, the team of David L. Applegate, Robert E. Bixby, Vašek Chvátal, William J. Cook developed one such solver, Concorde; the team was awarded The Beale-Orchard-Hays Prize for Excellence in Computational Mathematical Programming in 2000 for their ten-page paper enumerating some of Concorde's refinements of the branch and cut method that led to the solution of a 13,509-city instance and it was awarded the Frederick W. Lanchester Prize in 2007 for their book, The Traveling Salesman Problem: A Computational Study. Chvátal is known for proving the art gallery theorem, for researching a self-describing digital sequence, for his work with David Sankoff on the Chvátal–Sankoff constants controlling the behavior of the longest common subsequence problem on random inputs, for his work with Endre Szemerédi on hard instances for resolution theorem proving.
Vašek Chvátal. Linear Programming. W. H. Freeman. ISBN 978-0-7167-1587-0.. Japanese translation published by Keigaku Shuppan, Tokyo, 1986. C. Berge and V. Chvátal. Topics on Perfect Graphs. Elsevier. ISBN 978-0-444-86587-8. CS1 maint: Extra text: authors list David L. Applegate; the Traveling Salesman Problem: A Computational Study. Princeton University Press. ISBN 978-0-691-12993-8. CS1 maint: Multiple names: authors list Vašek Chvátal. Combinatorial Optimization: Methods and Applications. IOS Press. ISBN 978-1-60750-717-8. CS1 maint: Extra text: authors list Chvátal's home page
Yurii Nesterov is a Russian mathematician, an internationally recognized expert in convex optimization in the development of efficient algorithms and numerical optimization analysis. He is a professor at the University of Louvain. In 1977, Yurii Nesterov graduated in applied mathematics at Moscow State University. From 1977 to 1992 he was a researcher at the Central Economic Mathematical Institute of the Russian Academy of Sciences. Since 1993, he has been working at UCLouvain in the Department of Mathematical Engineering from the Louvain School of Engineering, Center for Operations Research and Econometrics. In 2000, Nesterov received the Dantzig Prize. In 2009, Nesterov won the John von Neumann Theory Prize. In 2016, Nesterov received the EURO Gold Medal. Nesterov is most famous for his work in convex optimization, including his 2004 book, considered a canonical reference on the subject, his main novel contribution is an accelerated version of gradient descent that converges faster than ordinary gradient descent.
His work with Arkadi Nemirovski in the 1994 book is the first to point out that the interior point method can solve convex optimization problems, the first to make a systematic study of semidefinite programming. In this book, they introduced the self-concordant functions which are useful in the analysis of Newton's method. Official website This article contains text translated from French Wikipedia
David Harold Blackwell was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, Bayesian statistics. He is one of the eponyms of the Rao–Blackwell theorem, he was the first African American inducted into the National Academy of Sciences, the first black tenured faculty member at UC Berkeley, the seventh African American to receive a Ph. D. in Mathematics. Blackwell was a pioneer in textbook writing, he wrote one of his 1969 Basic Statistics. By the time he retired, he had published over 90 books and papers on dynamic programming, game theory, mathematical statistics. David Harold Blackwell was born on April 24, 1919, in Centralia, Illinois to Mabel Johnson Blackwell, a full-time homemaker, Grover Blackwell, an Illinois Central Railroad worker, he was the eldest of four children. Growing up in an integrated community, Blackwell attended “mixed” schools, where he distinguished himself in mathematics. During elementary school, his teachers promoted him beyond his grade level on two occasions.
It was in a high school geometry course, that his passion for math began. An exceptional student, Blackwell graduated high school in 1935 at the age of sixteen. Blackwell entered the University of Illinois at Urbana-Champaign with the intent to study elementary school mathematics and become a teacher. In 1938 he earned his bachelor's degree in mathematics and a master's degree in 1939, was awarded a PhD in mathematics in 1941 at the age of 22, all by the University of Illinois. Blackwell was a member of Alpha Phi Alpha fraternity, he did a year of post-doctoral studies as a fellow at Institute for Advanced Study in 1941 after receiving a Rosenwald Fellowship. There he met John von Neumann, who asked Blackwell to discuss his Ph. D. thesis with him. Blackwell, who believed that von Neumann was just being polite and not genuinely interested in his work, did not approach him until von Neumann himself asked him again a few months later. According to Blackwell, "He listened to me talk about this rather obscure subject and in ten minutes he knew more about it than I did."He departed when he was prevented from attending lectures or undertaking research at nearby Princeton University because of his race.
Seeking a permanent position, he wrote letters of application to 105 black colleges and universities. He felt at the time, he sought a position at the University of California and was interviewed by statistician Jerzy Neyman. While Neyman supported his appointment, race-based objections prevented his appointment at that time, he was offered a post at Southern University at Baton Rouge, which he held in 1942–43, followed by a year as an Instructor at Clark College in Atlanta. He moved to Howard University in 1944 and within three years was appointed full professor and head of the Mathematics Department, he remained at Howard until 1954. From 1948 to 1950, Blackwell spent his summers at RAND Corporation with Meyer A. Girshick and other mathematicians exploring the theory of duels. In 1954 Girshick and Blackwell published Theory of Statistical Decisions. Blackwell wrote one of his 1969 Basic Statistics. Blackwell's Basic Statistics inspired the 1995 textbook Statistics: A Bayesian Perspective by the biostatician Donald Berry.
He took a position at the University of California, Berkeley as a visiting professor in 1954, was hired as a full professor in the newly created Statistics Department in 1955, becoming the Statistics department chair in 1956. He spent the rest of his career at UC Berkeley, retiring in 1988. In 2018, UC Berkeley named an undergraduate residence hall in his honor. David Blackwell Hall opened in Fall 2018. Blackwell married Ann Madison on December 27, 1944, they had eight children together. David Blackwell died of complications from a stroke on July 8, 2010 at Alta Bates Summit Medical Center in Berkeley, California. Don't worry about the overall importance of the problem. I think there's a sufficient correlation between importance. Invited Speaker at the International Congress of Mathematicians, 1954 President, Institute of Mathematical Statistics, 1956 National Academy of Sciences, 1965 American Academy of Arts and Sciences, 1968 President of the Bernoulli Society for Mathematical Statistics and Probability, 1975-1977 Honorary Fellow, Royal Statistical Society, 1976 Vice President, American Statistical Association, 1978 John von Neumann Theory Prize, 1979 R. A. Fisher Lectureship, 1986 The Berkeley Citation, 1988 National Medal of Science, 2012 The Blackwell-Tapia prize is named for Blackwell and Richard A. Tapia.
Kelly Miller C. R. Rao Biographical sketch from the American Statistical Association "Dr. David Blackwell Biography Packet".. provided by the Department of Statistics at the University of California, Berkeley. Archived from the original on June 22, 2010. David Blackwell's oral history video excerpts at The National Visionary Leadership Project On Google scholar "David Blackwell, Scholar of Probability, Dies at 91", New York Times David Blackwell at the Mathematics Genealogy Project A volume dedicated to David H. Blackwell, Celebratio Mathematica Biography of David Blackwell from the Institute for Operations Research and the Management Sciences
Martin Grötschel is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin and served from 2012 to 2015 as ZIB's President. Since October 2015 he has been President of the Berlin-Brandenburg Academy of Sciences and Humanities. Grötschel was born in Schwelm and earned a diploma in mathematics with minor in economics in 1973 from the University of Bochum, he completed a doctorate in 1977 at the University of Bonn under the supervision of Bernhard Korte, obtained his habilitation at Bonn in the field operations research in 1981. One year he was appointed full professor for applied mathematics at the University of Augsburg. From 1991 until his retirement at the end of September 2015 he was, while engaged at ZIB, full professor for information technology at Technical University Berlin. Martin Grötschel was a member of the Executive Committee of the German Mathematical Society from 1989 to 1996 and from 1993 to 1994 its President.
From 1999 to 2014 he was a member of the Executive Committee of the International Mathematical Union and from 2007 to 2014 IMU's General Secretary. Since 2011 he has been a member of the Executive Board of the Einstein Foundation Berlin and was from 2011 to 2015 its Chair, he was co-founder and longstanding Chair of the DFG Research Center Matheon "Mathematics for key technologies". Martin Grötschel has three daughters. Martin Grötschel is one of the most internationally renowned experts in the field of combinatorial optimization. Martin Grötschel's main mathematical research fields are graph theory and mixed-integer optimization and operations research. In his doctoral thesis, Grötschel achieved significant progress in the development of solution methods of the Traveling Salesman Problem, in particular, he contributed to understanding the cutting-plane method, his publications together with L. Lovász and A. Schrijver on the ellipsoid method and its application in the combinatorial and convex optimization gained worldwide recognition.
In recent years Martin Grötschel has dealt with mathematical modelling and solving real-world problems in economy and industry. The application areas he has worked in include optimization of production planning and control, public transport and energy systems and telecommunication. Since the early 1990s Grötschel has been working intensively in the fields electronic information and communication, library systems, Open Access and Open Science and thereto participated in numerous national and international bodies and initiatives; the promotion of digital humanities is one of the main goals of Grötschel's BBAW presidency. Grötschel was one of the winners of the Fulkerson Prize of the American Mathematical Society in 1982 for his work with László Lovász and Alexander Schrijver on applications of the ellipsoid method to combinatorial optimization. In 2006 the same trio won the John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences; the Society for Industrial and Applied Mathematics and Mathematical Optimization Society gave Grötschel the George B.
Dantzig Prize in 1991, the Deutsche Forschungsgemeinschaft gave him the Gottfried Wilhelm Leibniz Prize in 1995. In 2004 he was awarded the EURO Gold Medal, the highest distinction within Operations Research in Europe, he was an invited speaker at the 2006 International Congress of Mathematicians. Grötschel received honorary doctorates from the University of Karlsruhe in 2006, from the Vietnamese Academy of Sciences and Technology in 2007, from the Otto-von-Guericke-Universität Magdeburg in 2008 and from the University of Augsburg in 2011. Since 2011 he has been Distinguished Affiliated Professor of Technical University of Munich. Grötschel is member of seven national and international scientific academies: In 1995 he was a member the Berlin-Brandenburg Academy of Sciences and Humanities, in 1999 he became Foreign Member of the US National Academy of Engineering for "contributions to combinatorial optimization and its applications", since 2003 he has been a member of the Deutsche Akademie der Technikwissenschaften, since 2005 of the German National Academy of Sciences Leopoldina, since 2015 of the Chinese Academy of Sciences as Foreign Member, since 2016 of The World Academy of Sciences for the advancement of science in the developing countries as Fellow, in 2017 he was elected a member of the Academy of Europe Academia Europaea.
In 2013, a festschrift was published in his honor. With Volker Mehrmann, Klaus Lucas: Production Factor Mathematics, Springer, 2010. With Alexander Schrijver, Lászlo Lovász: Geometric algorithms and combinatorial optimization, Springer 1988, 2nd edition 1993. With R. L. Graham, L. Lovász: Handbook of Combinatorics. 2 Vols. MIT Press, Elsevier, 1995. Grötschel's homepage at Zuse Institute Berlin