Adi Ben-Israel (Hebrew: עדי בן-ישראל, born November 6, 1933) is a

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 an

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

, working in

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

, optimization,

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation 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 other areas. He is a Professor of Operations Research at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

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, southeast, and south by the Atlantic Ocean; on the west by the Delaware ...

Research topics

Ben-Israel's research has included

generalized inverse In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inv ...

s of

matrice Matrice is a ''comune'' (municipality) in the Province of Campobasso in the Italian region Molise, located about northeast of Campobasso. As of 31 December 2004, it had a population of 1,081 and an area of .All demographics and other statistics: ...

s, in particular the Moore–Penrose pseudoinverse, and of operators, their extremal properties,

computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An es ...

and applications. as well as local inverses of

nonlinear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...

mappings. In the area of

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. ...

, he studied the matrix volume and its applications, basic, approximate and least-norm solutions, and the geometry of subspaces. He wrote about ordered

incidence geometry In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An ''incidenc ...

and the geometric foundations of convexity. In the topic of iterative methods, he published papers about the

Newton method In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...

for systems of equations with rectangular or singular Jacobians, directional Newton methods, the quasi-Halley method, Newton and Halley methods for complex roots, and the inverse Newton transform. Ben-Israel's research into optimization included linear programming, a Newtonian bracketing method of

convex minimization Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization pro ...

, input optimization, and risk modeling of

dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

, and the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

. He also studied various aspects of clustering and location theory, and investigated decisions under uncertainty.

Publications

Books * ''Generalized Inverses: Theory and Applications'', with T.N.E. Greville, J. Wiley, New York, 1974 * ''Optimality in Nonlinear Programming: A Feasible Directions Approach'', with A. Ben-Tal and S. Zlobec, J. Wiley, New York, 1981 * ''Mathematik mit DERIVE'' (German), with W. Koepf and R.P. Gilbert, Vieweg-Verlag, Berlin, , 1993 * ''Computer Supported Calculus: With MACSYMA'', with R.P. Gilbert,

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, Vienna, , 2001 * ''Generalized Inverses: Theory and Applications'' (2nd edition), with T.N.E. Greville, Springer-Verlag, New York, , 2003 Selected articles * Contributions to the theory of generalized inverses, ''J. Soc. Indust. Appl. Math.'' 11(1963), 667–699, (with A. Charnes) * A Newton–Raphson method for the solution of systems of equations, ''J. Math. Anal. Appl.'' 15(1966), 243–252 * Linear equations and inequalities on finite-dimensional, real or complex, vector spaces: A unified theory, ''J. Math. Anal. Appl.'' 27(1969), 367–389 * Ordered incidence geometry and the geometric foundations of convexity theory, ''J. Geometry'' 30(1987), 103–122, (with A. Ben-Tal) * Input optimization for infinite horizon discounted programs, ''J. Optimiz. Th. Appl.'' 61(1989), 347–357, (with S.D. Flaam) * Certainty equivalents and information measures: Duality and extremal principles, ''J. Math. Anal. Appl.'' 157(1991), 211–236 (with A. Ben-Tal and M. Teboulle). * A volume associated with mxn matrices, ''Lin. Algeb. and Appl.'' 167(1992), 87–111.
The Moore of the Moore–Penrose inverse
''Electron. J. Lin. Algeb.'' 9(2002), 150–157. * The Newton bracketing method for convex minimization, ''Comput. Optimiz. and Appl.'' 21(2002), 213–229 (with Y. Levin). * An inverse Newton transform, ''Contemporary Math.'' 568(2012), 27–40.
A concentrated Cauchy distribution with finite moments
''Annals of Oper. Res.'' (to appear)

References

External links

Adi Ben-Israel
at the Mathematics Genealogy Project {{DEFAULTSORT:Ben-Israel, Adi Rutgers University faculty Living people 1933 births American mathematicians Place of birth missing (living people)