James Renegar

Last updated

James Milton Renegar Jr. (born May 14, 1955) is an American mathematician, specializing in optimization algorithms for linear programming and nonlinear programming.

Contents

Biography

In 1983 he received his Ph.D. in mathematics from the University of California, Berkeley. His Ph.D. thesis On the Computational Complexity of Simplicial Algorithms in Approximation Zeros of Complex Polynomials was supervised by Stephen Smale. [1] After postdoc positions, Renegar joined in 1987 the faculty of the School of Operations Research and Information Engineering at Cornell University and is now a full professor there. [2]

Renegar is a leading expert on optimization algorithms. In recent years, the focus of his research is devising new algorithms for linear programming. [3] He has done research on 'interior-point methods for convex optimization (for which he wrote a well-known introductory monograph), quantifier elimination methods for the first-order theory of the reals, development of the notion of "condition number" in the context of general conic optimization problems, algorithms for hyperbolic programming, and most recently, the discovery of a simple paradigm for solving general convex conic optimization problems by first-order methods.' [2] His 2001 monograph A Mathematical View of Interior-point Methods in Convex Optimization is intended to present a general theory of interior-point methods, suitable for a wide audience of graduate students in mathematics and engineering. [4] [5]

In 1990 Renegar was an invited speaker at the International Congress of Mathematicians in Kyoto. [6] In 1995 he was a founding member of the nonprofit organization Foundations of Computational Mathematics. [2] He was awarded the 2018 Khachiyan Prize. [7]

James M. Renegar Jr. married Catharine M. Barnaby and is the father of two children, Alice and Nicholas James. James M. Renegar Sr. (1928–2005) practiced law in Oklahoma City for many years. [8]

Selected publications

Articles

Books

Related Research Articles

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming.

Convex hull Smallest convex set containing a given set

In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset.

Linear programming Method to solve some optimization problems

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.

Mathematical optimization Study of mathematical algorithms for optimization problems

Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Time complexity Estimate of time taken for running an algorithm

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

Narendra Krishna Karmarkar is an Indian Mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher.

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.

The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.

Interior-point method Algorithms for solving convex optimization problems

Interior-point methods are a certain class of algorithms that solve linear and nonlinear convex optimization problems.

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

Ellipsoid method

In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size.

Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry.

The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraints. It also relates to inductive reasoning in modeling and decision-making. The technique has existed for decades as a heuristic approach and has more recently been given a systematic theoretical foundation.

Integral polytope

In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex hull of its integer points. Integral polytopes are also called lattice polytopes or Z-polytopes. The special cases of two- and three-dimensional integral polytopes may be called polygons or polyhedra instead of polytopes, respectively.

In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form

Criss-cross algorithm

In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming problems, quadratic-programming problems, and linear complementarity problems.


Peter Richtarik is a Slovak mathematician and computer scientist working in the area of big data optimization and machine learning, known for his work on randomized coordinate descent algorithms, stochastic gradient descent and federated learning. He is currently a Professor of Computer Science at the King Abdullah University of Science and Technology.

Adrian Stephen Lewis is a British-Canadian mathematician, specializing in variational analysis and nonsmooth optimization.

Shmuel Onn Israeli mathematician

Shmuel Onn is a mathematician, Professor of Operations Research and Dresner Chair at the Technion - Israel Institute of Technology. He is known for his contributions to integer programming and nonlinear combinatorial optimization.

In convex geometry and polyhedral combinatorics, the extension complexity is a convex polytope is the smallest number of facets among convex polytopes that have as a projection. In this context, is called an extended formulation of ; it may have much higher dimension than .

References

  1. James Milton Renegar, Jr. at the Mathematics Genealogy Project
  2. 1 2 3 "Jim Renegar". Simons Institute for the Theory of Computing.
  3. "James Renegar, Professor". Department of Mathematics, Cornell University.
  4. Renegar, James (1 January 2001). "Preface". A Mathematical View of Interior-point Methods in Convex Optimization. SIAM. p. vii. ISBN   978-0-89871-881-2.
  5. Freund, Robert M. (2003). "Book Review: A mathematical view of interior-point methods in convex optimization". Mathematics of Computation. 73 (245): 515–516. doi: 10.1090/S0025-5718-03-01659-4 . ISSN   0025-5718.
  6. "ICM Plenary and Invited Speakers". International Mathematical Union.
  7. "James Renegar is selected as the winner of the 2018 INFORMS Optimization Society Khachiyan Prize". INFORMS Optimization Society.
  8. "James Milton Renegar". The Oklahoman. March 2005.