Robert J. Vanderbei
Encyclopedia
Robert J. Vanderbei is an American mathematician
and Professor in the Department of Operations Research
and Financial Engineering at Princeton University
.
and his PhD in Applied Mathematics from Cornell University
in 1981. In his thesis, he developed probabilistic potential theory for random fields consisting of tensor products of Brownian motions
. He was postdoctoral research fellow at New York University
's Courant Institute of Mathematical Sciences
and then at the Mathematics Department at the University of Illinois in Urbana-Champaign. In 1984, he left academia and joined Bell Labs
, where he served as a team member of AT&T
's Advanced Decision Support Systems venture. In 1990, Vanderbei returned to academia to teach at Princeton University
. He is currently a full professor in the Department of Operations Research and Financial Engineering (ORFE). Since July 2005, he has been chair of the department. In addition to his appointment in ORFE, he also has courtesy appointments in Mathematics, Astrophysics, Computer Science, and Applied Mathematics. He is also a member of the Bendheim Center for Finance
.
discovery of a new polynomial-time algorithm for linear programming
. In May 1985, he became the first nonmanagement team member of AT&T
's Advanced Decision Support Systems venture, where he served as the interface to Karmarkar
and as the lead developer of the first release of the linear programming
software.
In 1985, Vanderbei, with Bell Labs colleagues Marc Meketon and Barry Freedman, wrote a paper proving convergence of a variant of Karmarkar's algorithm
that became known as the Affine-Scaling algorithm. Eventually it became known that I.I. Dikin, working in Siberia
and publishing in Russian
, had proved convergence of the same algorithm under weaker nondegeneracy assumptions many years earlier. Vanderbei, both individually and with Meketon, and Freedman was awarded US Patents for his theoretical and practical work on the affine-scaling algorithm. Taken together with the three patents awarded to Karmarkar
, this suite of patents represented the first awarded for what was considered pure mathematics
. At the time, they generated loud objections from other researchers in optimization algorithms.
In 1987, Vanderbei left the development team and moved to the Bell Labs' Math Research Center in Murray Hill, NJ. In 1990, he returned to academia to teach at Princeton University. Throughout the 1990s Vanderbei, in collaboration with David Shanno and graduate students, extended the so-called interior-point paradigm
from linear optimization problems
first to quadratic problems
, then to convex, and finally to nonlinear optimization problems
.
In 1993, Helmberg, Rendl, Vanderbei, and Wolkowicz wrote one of the first papers on interior-point methods
for semidefinite programming
(SDP), wherein they developed an algorithm for SDP and reported some preliminary computational results. The HKM search direction proposed in this paper is still widely used and outperforms other approaches. The paper is one of the most cited papers in the field of semidefinite programming.
In 1995, Vanderbei co-authored a paper on robust optimization
with John Mulvey and Stavros Zenios. In 2000, Ben-Tal and Nemirovsky wrote a follow-up paper on the subject, which launched robust optimization as an important subfield of optimization. The Mulvey-Vanderbei-Zenios paper stands as one of the most frequently referenced papers on robust optimization.
Vanderbei is the author of a textbook on linear programming and a software package for nonlinear programming
called LOQO.
course. The US News and World Report magazine, among other media outlets, reprinted his so-called Purple America
map, which he made after the 2000 US Presidential election
(and then subsequent national elections) to depict on a county-by-county
level how the elections turned out.
s, PIAA-style pupil mapping coronagraph
s, and space-based external occulters. Together with J. Richard Gott
, Vanderbei is the author of a forthcoming National Geographic book called Sizing Up The Universe (Book website).
for the Central Jersey
Soaring
Club. In 1999, he retired from soaring and took up the hobby of astrophotography
. He regularly posts new astroimages on his astro gallery website.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and Professor in the Department of Operations Research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
and Financial Engineering at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
Biography
Robert J. Vanderbei received his BS in Chemistry in 1976 and an MS in Operations Research and Statistics in 1978 from Rensselaer Polytechnic InstituteRensselaer Polytechnic Institute
Stephen Van Rensselaer established the Rensselaer School on November 5, 1824 with a letter to the Rev. Dr. Samuel Blatchford, in which van Rensselaer asked Blatchford to serve as the first president. Within the letter he set down several orders of business. He appointed Amos Eaton as the school's...
and his PhD in Applied Mathematics from Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
in 1981. In his thesis, he developed probabilistic potential theory for random fields consisting of tensor products of Brownian motions
Wiener process
In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called standard Brownian motion, after Robert Brown...
. He was postdoctoral research fellow at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
's Courant Institute of Mathematical Sciences
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
and then at the Mathematics Department at the University of Illinois in Urbana-Champaign. In 1984, he left academia and joined Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
, where he served as a team member of AT&T
AT&T
AT&T Inc. is an American multinational telecommunications corporation headquartered in Whitacre Tower, Dallas, Texas, United States. It is the largest provider of mobile telephony and fixed telephony in the United States, and is also a provider of broadband and subscription television services...
's Advanced Decision Support Systems venture. In 1990, Vanderbei returned to academia to teach at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. He is currently a full professor in the Department of Operations Research and Financial Engineering (ORFE). Since July 2005, he has been chair of the department. In addition to his appointment in ORFE, he also has courtesy appointments in Mathematics, Astrophysics, Computer Science, and Applied Mathematics. He is also a member of the Bendheim Center for Finance
Bendheim Center for Finance
The Bendheim Center for Finance is an interdisciplinary research center established by Princeton University in 1998. -History:In 1998, Princeton University established the Bendheim Center for Finance to encourage interdisciplinary research in finance from a quantitative or mathematical perspective...
.
Mathematical Programming
Vanderbei’s arrival at Bell Labs coincided with Narendra Karmarkar’sNarendra Karmarkar
Narendra K. Karmarkar is an Indian mathematician, renowned for developing Karmarkar's algorithm. He is listed as an ISI highly cited researcher.- Biography :...
discovery of a new polynomial-time algorithm for linear programming
Karmarkar's algorithm
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time...
. In May 1985, he became the first nonmanagement team member of AT&T
AT&T
AT&T Inc. is an American multinational telecommunications corporation headquartered in Whitacre Tower, Dallas, Texas, United States. It is the largest provider of mobile telephony and fixed telephony in the United States, and is also a provider of broadband and subscription television services...
's Advanced Decision Support Systems venture, where he served as the interface to Karmarkar
Narendra Karmarkar
Narendra K. Karmarkar is an Indian mathematician, renowned for developing Karmarkar's algorithm. He is listed as an ISI highly cited researcher.- Biography :...
and as the lead developer of the first release of the linear programming
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
software.
In 1985, Vanderbei, with Bell Labs colleagues Marc Meketon and Barry Freedman, wrote a paper proving convergence of a variant of Karmarkar's algorithm
Karmarkar's algorithm
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time...
that became known as the Affine-Scaling algorithm. Eventually it became known that I.I. Dikin, working in Siberia
Siberia
Siberia is an extensive region constituting almost all of Northern Asia. Comprising the central and eastern portion of the Russian Federation, it was part of the Soviet Union from its beginning, as its predecessor states, the Tsardom of Russia and the Russian Empire, conquered it during the 16th...
and publishing in Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
, had proved convergence of the same algorithm under weaker nondegeneracy assumptions many years earlier. Vanderbei, both individually and with Meketon, and Freedman was awarded US Patents for his theoretical and practical work on the affine-scaling algorithm. Taken together with the three patents awarded to Karmarkar
Narendra Karmarkar
Narendra K. Karmarkar is an Indian mathematician, renowned for developing Karmarkar's algorithm. He is listed as an ISI highly cited researcher.- Biography :...
, this suite of patents represented the first awarded for what was considered pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
. At the time, they generated loud objections from other researchers in optimization algorithms.
In 1987, Vanderbei left the development team and moved to the Bell Labs' Math Research Center in Murray Hill, NJ. In 1990, he returned to academia to teach at Princeton University. Throughout the 1990s Vanderbei, in collaboration with David Shanno and graduate students, extended the so-called interior-point paradigm
Interior point method
Interior point methods are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann...
from linear optimization problems
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
first to quadratic problems
Quadratic programming
Quadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....
, then to convex, and finally to nonlinear optimization problems
Nonlinear programming
In mathematics, nonlinear programming is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are...
.
In 1993, Helmberg, Rendl, Vanderbei, and Wolkowicz wrote one of the first papers on interior-point methods
Interior point method
Interior point methods are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann...
for semidefinite programming
Semidefinite programming
Semidefinite programming is a subfield of convex optimization concerned with the optimization of a linear objective functionover the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron....
(SDP), wherein they developed an algorithm for SDP and reported some preliminary computational results. The HKM search direction proposed in this paper is still widely used and outperforms other approaches. The paper is one of the most cited papers in the field of semidefinite programming.
In 1995, Vanderbei co-authored a paper on robust optimization
Robust optimization
Robust optimization is a field of optimization theory that deals with optimization problems where robustness is sought against uncertainty and/or variability in the value of a parameter of the problem.- History :...
with John Mulvey and Stavros Zenios. In 2000, Ben-Tal and Nemirovsky wrote a follow-up paper on the subject, which launched robust optimization as an important subfield of optimization. The Mulvey-Vanderbei-Zenios paper stands as one of the most frequently referenced papers on robust optimization.
Vanderbei is the author of a textbook on linear programming and a software package for nonlinear programming
Nonlinear programming
In mathematics, nonlinear programming is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are...
called LOQO.
Purple America
Vanderbei received widespread attention for something that was only intended to be an exercise for the freshman computer programmingComputer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...
course. The US News and World Report magazine, among other media outlets, reprinted his so-called Purple America
Purple America
The phrase Purple America refers to the belief that a more detailed analysis of the voting results of recent United States national elections reveals that the U.S. electorate is not as polarized between "Red" America and "Blue" America as is often depicted in news analysis...
map, which he made after the 2000 US Presidential election
United States presidential election, 2000
The United States presidential election of 2000 was a contest between Republican candidate George W. Bush, then-governor of Texas and son of former president George H. W. Bush , and Democratic candidate Al Gore, then-Vice President....
(and then subsequent national elections) to depict on a county-by-county
County (United States)
In the United States, a county is a geographic subdivision of a state , usually assigned some governmental authority. The term "county" is used in 48 of the 50 states; Louisiana is divided into parishes and Alaska into boroughs. Parishes and boroughs are called "county-equivalents" by the U.S...
level how the elections turned out.
Recent Research Interests
Since 2001, most of Vanderbei's research has been devoted to developing high-contrast imaging systems with the eventual aim of direct imaging of exoplanets. The concepts he has contributed to include shaped-pupil coronagraphCoronagraph
A coronagraph is a telescopic attachment designed to block out the direct light from a star so that nearby objects – which otherwise would be hidden in the star's bright glare – can be resolved...
s, PIAA-style pupil mapping coronagraph
Coronagraph
A coronagraph is a telescopic attachment designed to block out the direct light from a star so that nearby objects – which otherwise would be hidden in the star's bright glare – can be resolved...
s, and space-based external occulters. Together with J. Richard Gott
J. Richard Gott
John Richard Gott III is a professor of astrophysical sciences at Princeton University. He is known for developing and advocating two cosmological theories with the flavor of science fiction: Time travel and the Doomsday argument.- Exotic matter time travel theories :Paul Davies's bestseller How...
, Vanderbei is the author of a forthcoming National Geographic book called Sizing Up The Universe (Book website).
Other Interests
Vanderbei also was a serious glider pilot for many years. From 1988 to 1999 he was chief flight instructorFlight instructor
A flight instructor is a person who teaches others to fly aircraft. Specific privileges granted to holders of a flight instructor qualification vary from country to country, but very generally, a flight instructor serves to enhance or evaluate the knowledge and skill level of an aviator in pursuit...
for the Central Jersey
Central Jersey
Central Jersey is a common designation for a region of the state of New Jersey in the United States of America. Trenton is considered the boundary between designated "North Jersey" and "South Jersey"...
Soaring
Lift (soaring)
Gliding flight is heavier-than-air flight without the use of thrust. It is employed by gliding animals and by aircraft such as gliders. The most common human application of gliding flight is in sport and recreation using aircraft designed for this purpose...
Club. In 1999, he retired from soaring and took up the hobby of astrophotography
Astrophotography
Astrophotography is a specialized type of photography that entails recording images of astronomical objects and large areas of the night sky. The first photographs of an astronomical object were taken in the 1840s, but it was not until the late 19th century that advances in technology allowed for...
. He regularly posts new astroimages on his astro gallery website.