[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.
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.
[6] In 1995 he was a founding member of the nonprofit organization Foundations of Computational Mathematics.