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, structure, space, models, and change. History On ...

and Professor in the Department of

Operations Research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...

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 mathema ...

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

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 research university in Troy, New York, with an additional campus in Hartford, Connecticut. A third campus in Groton, Connecticut closed in 2018. RPI was established in 1824 by Stephen Van ...

and his PhD in Applied Mathematics from

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

in 1981. In his thesis, he developed probabilistic potential theory for

random fields In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as \mathbb^n). That is, it is a function f(x) that takes on a random value at each point x \in \mathbb^n(or some other ...

consisting of

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

of Brownian motions. He was postdoctoral research fellow at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

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), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

and then at the Mathematics Department at the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

. In 1984, he left academia and joined

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

, where he served as a team member of

AT&T AT&T Inc. is an American multinational telecommunications holding company headquartered at Whitacre Tower in Downtown Dallas, Texas. It is the world's largest telecommunications company by revenue and the third largest provider of mobile tel ...

'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 and is dedicated to research and education in the area of money and finance, in lieu of there ...

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 Circa 1956) is an Indian Mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear prog ...

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 are represented by linear function#As a polynomial function, li ...

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 ( ; rus, Сибирь, r=Sibir', p=sʲɪˈbʲirʲ, a=Ru-Сибирь.ogg) is an extensive geographical region, constituting all of North Asia, from the Ural Mountains in the west to the Pacific Ocean in the east. It has been a part of ...

and publishing in

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

, 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 definiti ...

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 northern New Jersey, United States. It is the longtime central location of Bell Labs (part of Nokia sin ...

. 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 convex optimization 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 positive ...

. 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 polytope ...

, 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 or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or sta ...

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 is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as ana ...

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 U.S. states whose voters vote predominantly for one party — the Republican Party in red states and the Democratic Party in ...

'' map, which he made after the

2000 US Presidential election The 2000 United States presidential election was the 54th quadrennial presidential election, held on Tuesday, November 7, 2000. Republican candidate George W. Bush, the governor of Texas and eldest son of the 41st president, George H. W. Bush, ...

(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 possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...

. 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 so that nearby objects – which otherwise would be hidden in the star's bright glare – can be resolved. Most coronagraphs are intended to view ...

s, PIAA-style pupil mapping

s, and space-based external

occulter An occulting disk is a small disk used in a telescope to block the view of a bright object in order to allow observation of a fainter one. The coronagraph, at its simplest, is an occulting disk in the focal plane of a telescope, or in front of th ...

s. Together with

J. Richard Gott John Richard Gott III (born February 8, 1947) is a professor of astrophysics, astrophysical sciences at Princeton University. He is known for his work on time travel and the Doomsday argument. Exotic matter time travel theories Paul Davies's ...

, Vanderbei is the author of a

National Geographic ''National Geographic'' (formerly the ''National Geographic Magazine'', sometimes branded as NAT GEO) is a popular American monthly magazine published by National Geographic Partners. Known for its photojournalism, it is one of the most widely ...

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

Other interests

Vanderbei also was a serious

glider pilot Glider 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 of glidin ...

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 is the central region of the U.S. state of New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, ...

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 1840, 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 concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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 (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

. In 2013 he became a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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".2014 Class of the Fellows of the AMS

, retrieved 2014-08-12.

References

This article incorporates material fro
Robert J. Vanderbei's bio
which is licensed under the

Creative Commons Attribution/Share-Alike License A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted "work".A "work" is any creative material made by a person. A painting, a graphic, a book, a song/lyrics ...

. * {{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