Robert J. Vanderbei (born 1955) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and Emeritus Professor in the Department of

Operations Research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...

and

Financial Engineering Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathe ...

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

Biography

Robert J. Vanderbei was born in Grand Rapids, MI, in 1955. He received his BS in Chemistry in 1976 and an MS in Operations Research and Statistics in 1978 from

Rensselaer Polytechnic Institute Rensselaer Polytechnic Institute (; RPI) is a private university, private research university in Troy, New York, United States. It is the oldest technological university in the English-speaking world and the Western Hemisphere. It was establishe ...

and his PhD in Applied Mathematics from

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

in 1981. In his thesis, he developed probabilistic potential theory for random fields consisting of

tensor products In mathematics, the tensor product V \otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of ...

of Brownian motions. He was postdoctoral research fellow at

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

and then at the Mathematics Department at the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public university, public land-grant university, land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United ...

. In 1984, he left academia and joined

Bell Labs Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...

, where he served as a team member of

AT&T AT&T Inc., an abbreviation for its predecessor's former name, the American Telephone and Telegraph Company, is an American multinational telecommunications holding company headquartered at Whitacre Tower in Downtown Dallas, Texas. It is the w ...

's Advanced Decision Support Systems venture. In 1990, Vanderbei returned to academia to teach at

. He is currently a Professor in the Department of Operations Research and Financial Engineering (ORFE). 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 (BCF) is an interdisciplinary center at Princeton University. It was established in 1997 at the initiative of Ben Bernanke. Yacine Ait-Sahalia served as the Center's inaugural director (1998-2014). The Center is dedica ...

Research

Mathematical programming

Vanderbei’s arrival at Bell Labs coincided with Narendra Karmarkar’s discovery of a new polynomial-time algorithm for linear programming. In May 1985, he became the first nonmanagement team member of

's Advanced Decision Support Systems venture, where he served as the interface to

Karmarkar Narendra Krishna Karmarkar (born 1956) is an Indian mathematician. He developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first probably Time complexity, polynomial time algorithms for linear ...

and as the lead developer of the first release of the

linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...

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 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. The ellipsoid method is also pol ...

that became known as the Affine-Scaling algorithm. Eventually it became known that I.I. Dikin, working in

Siberia Siberia ( ; , ) is an extensive geographical region comprising all of North Asia, from the Ural Mountains in the west to the Pacific Ocean in the east. It has formed a part of the sovereign territory of Russia and its predecessor states ...

and publishing in

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

, had proved convergence of the same algorithm under weaker

nondegeneracy In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space ''V'' is a bilinear form such that the map from ''V'' to ''V''∗ (the dual space of ''V'') given by is not an isomorphism. An equivalent definition when ' ...

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

, this suite of patents represented the first awarded for what was considered

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

. 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 Murray Hill is an unincorporated community located within portions of both Berkeley Heights and New Providence, located in Union County, in the northern portion of the U.S. state of New Jersey. It is the longtime central location of Bell Lab ...

. In 1990, he returned to academia to teach at Princeton University. Throughout the 1990s Vanderbei's research governed the development of interior-point solvers. In 1993, Helmberg, Rendl, Vanderbei, and Wolkowicz developed an interior-point algorithm for

semidefinite programming Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of po ...

. Vanderbei later developed algorithms for quadratic problems,

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

, and finally nonlinear optimization problems. Vanderbei is the author of a textbook on linear programming and a software package for

nonlinear programming In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation ...

calle
LOQO

Purple America

Vanderbei received widespread attention for something that was only intended to be an exercise for the freshman

computer programming Computer programming or coding is the composition of sequences of instructions, called computer program, programs, that computers can follow to perform tasks. It involves designing and implementing algorithms, step-by-step specifications of proc ...

course. '' U.S. News & World Report'' magazine, among other media outlets, reprinted his so-called ''

Purple America Starting with the 2000 United States presidential election, the terms "red state" and "blue state" have referred to US states whose voters vote predominantly for one party—the Republican Party in red states and the Democratic Party in blue ...

'' map, which he made after the

2000 US Presidential election Presidential elections were held in the United States on November 7, 2000. Republican Governor George W. Bush of Texas, the eldest son of 41st President George H. W. Bush, and former Secretary of Defense Dick Cheney narrowly defeated incumbe ...

(and then subsequent national elections) to depict on a county-by-county 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 An exoplanet or extrasolar planet is a planet outside the Solar System. The first confirmed detection of an exoplanet was in 1992 around a pulsar, and the first detection around a main-sequence star was in 1995. A different planet, first detec ...

. The concepts he has contributed to include shaped-pupil

coronagraph A coronagraph is a telescopic attachment designed to block out the direct light from a star or other bright object so that nearby objects – which otherwise would be hidden in the object's bright glare – can be resolved. Most coronagr ...

s, PIAA-style pupil mapping

s, and space-based external occulters. Together with J. Richard Gott, Vanderbei is the author of a

National Geographic ''National Geographic'' (formerly ''The National Geographic Magazine'', sometimes branded as ''Nat Geo'') is an American monthly magazine published by National Geographic Partners. The magazine was founded in 1888 as a scholarly journal, nine ...

book called ''Sizing Up The Universe''
Book website
.

Other interests

Vanderbei also was a serious

glider pilot Glider or Gliders may refer to: Aircraft and transport Aircraft * Glider (aircraft), heavier-than-air aircraft primarily intended for unpowered flight ** Glider (sailplane), a rigid-winged glider aircraft with an undercarriage, used in the sport ...

for many years. From 1988 to 1999 he was chief

flight instructor A flight instructor is a person who teaches others to operate 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 ...

for the

Central Jersey Central Jersey, or Central New Jersey, is the middle region of the U.S. state of New Jersey. The designation Central Jersey is a distinct administrative toponym. While New Jersey is often divided into North Jersey and South Jersey, many resi ...

Soaring Soaring may refer to: * Gliding, in which pilots fly unpowered aircraft known as gliders or sailplanes * Lift (soaring), a meteorological phenomenon used as an energy source by some aircraft and birds * ''Soaring'' (magazine), a magazine produced ...

Club. In 1999, he retired from soaring and took up the hobby of

astrophotography Astrophotography, also known as astronomical imaging, is the photography or imaging of astronomical objects, celestial events, or areas of the night sky. The first photograph of an astronomical object (the Moon) was taken in 1839, but it was no ...

. He regularly posts new astroimages on hi
astro gallery website

Awards and honors

He was elected to the 2006 class of

Fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often s ...

. In 2012 he became a

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

of the

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...

for "contributions to technologies for exoplanet searches and to interior-point methods for nonlinear optimization". In 2014 he became a

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, for "contributions to linear programming and nonlinear optimization problems". In 2017 he was award the Khachiyan Prize by the

INFORMS The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often s ...

Optimization Society.Robert Vanderbei is selected as the winner of the 2017 INFORMS Optimization Society Khachiyan Prize
/ref>

References

This article incorporates material fro

which is licensed under the

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. * {{DEFAULTSORT:Vanderbei, Robert J. 1955 births Living people Rensselaer Polytechnic Institute alumni Cornell University alumni Princeton University faculty American operations researchers American computer scientists Fellows of the American Mathematical Society Fellows of the Institute for Operations Research and the Management Sciences Fellows of the Society for Industrial and Applied Mathematics People from Grand Rapids, Michigan 20th-century American mathematicians 21st-century American mathematicians