Algorithms, Optimization

Office: 231 Rhodes

Phone: 607.255.9142

Fax: 607.255.9129

James Renegar Professor James Renegar received his B. A. from Rice University in 1976 and his Ph.D. in Mathematics from the University of California at Berkeley in 1983. Professor Renegar joined the faculty of the School of Operations Research and Industrial Engineering in 1987. Prior to this, Renegar was an NSF Mathematical Sciences Postdoctoral Research Fellow and Assistant Professor in the Department of Mathematics at Colorado State University.

Renegar’s research focus is in continuous mathematical programming. Professor Renegar typically gravitates to algorithmic problems possessing an interplay of numerical analysis and algebra (e.g., approximating roots of polynomials, decision and quantifier elimination methods for the first-order theory of the reals, interior-point methods for algebraic convex optimization problems). He has laid theoretical foundations for round-off error analysis of algorithms for convex optimization. Currently he is pursuing hyperbolic programming, where he is devising algorithms that generalize interior-point methods.

He is also interested in continuous optimization problems having thorough differential-manifold or algebraic structure, such as problems whose constraint functions are multivariate polynomials. He also is intrigued by optimization problems that are naturally viewed from the perspective of functional analysis and its rich duality theory. Presently he is investigating sequences of relaxations of hyperbolic programming problems, of which linear programming and semidefinite programming are special cases.

Select Publications

“Hyperbolic programs, and their derivative relaxations”. To appear in Foundations of Computational Mathematics.

“A Mathematical View of Interior-Point Methods for Convex Optimization”. MPS-SIAM Series on Optimization, Philadelphia (2001).

“Computing approximate solutions for convex conic systems of constraints”. Mathematical Programming 87, 351- 384 (2000). (With J. Pena)

“Condition numbers, the barrier method and the conjugate gradient method”. SIAM Journal on Optimization 6, 879 - 912 (1996).

“Linear programming , complexity theory and elementary functional analysis”. Mathematical Programming 70, 279 - 351 (1995).

 “Some Perturbation theory for linear programming”. Mathematical Programming 65, 73 - 91 (1994).

Lectures

Seventeenth International Symposium on Mathematical Programming, Atlanta, August 2000.

International Conference on Foundation of Computational Mathematics, Hong Kong, July 2000.

Fourth International Conference on High Performance Optimization Techniques, Rotterdam, The Netherlands, June, 1999.

Distinguished Lecture Series, Center for Operations Research and Econometrics, Universite Catholique de Louvain, Belgium, 1996.

Professional Activities

Society for Foundations of Computational Mathematics

INFORMS Lancaster Prize Committee, 2001- 2002 Chairman

INFORMS Lancaster Prize Committee, 2002

Associate Editor, SIAM Journal on Optimization, 1995 - 2001

University Activities

Director of the School of Operations Research and Industrial Engineering 2004 - present

Awards and Recognition

Founding member, Board of Directors and Treasurer for the Society for Foundations of Computational Mathematics (FOCM), 1995 - present

College of Engineering Sonny Yau Excellence in Teaching Award, 1998 and 2001