[Ml-stat-talks] Princeton Optimization Seminar: James Renegar, Cornell -- Thursday, April 21, 4:30 PM

Amir Ali Ahmadi a_a_a at princeton.edu
Sun Apr 17 01:48:10 EDT 2016

-----   Princeton Optimization Seminar   -----

DATE: Thursday, April 21, 2016

TIME:  4:30 PM

LOCATION:  Sherrerd Hall 101

SPEAKER: James Renegar, Cornell University

TITLE: Applying First-Order Methods to Solve General Convex Conic Optimization Problems<https://orfe.princeton.edu/abstracts/optimization-seminar/applying-first-order-methods-solve-general-convex-conic-optimization>

Recently we introduced a framework for applying subgradient methods to solve general convex, conic optimization problems. The framework, once seen, is obvious, but had not appeared in the literature, a blind spot. More recently we posted a refinement of the framework in the special case of hyperbolic programming, a generalization of semidefinite programming. Hyperbolicity cones have algebraic structure ideal for smoothing. Once a hyperbolic program is smoothed, virtually any accelerated method can be applied, which if done with care, results in a first-order algorithm with best-possible iteration bound. We provide an overview of these developments, then briefly discuss where we are now working to deepen and broaden the results, both in the pure theory and with regards to design of algorithms aimed at practice.

James Renegar is a Professor in the School of Operations Research and Information Engineering at Cornell University, where he has been since 1987, after receiving a PhD in Mathematics from Berkeley under the guidance of Steve Smale. Throughout his career, Renegar's research has focused on algorithms -- especially on their theory -- including, among other topics, 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, discovery of a simple paradigm for solving general convex conic optimization problems by first-order methods. Renegar was one of five founding members in 1995 of the Society for Foundations of Computational Mathematics. He long served on its Board of Directors, and also has served in a multitude of other capacities, including his current role as associate editor for the society's journal.

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