Sunday, May 18, 5:00 – 7:00 PM
Garden Salon 2
Welcome
Marina Epelman
University of Michigan, mepelman@umich.edu
Greedy Algorithms and Dual Averaging: Structural Connections and Computational Guarantees
Paul Grigas
Massachusetts Institute of Technology, pgrigas@mit.edu
Especially in huge-scale applications, greedy first-order algorithms offer relatively low computational requirements per iteration in addition to other appealing computational properties. In this talk, we discuss precise connections between the dual averaging method for non-smooth optimization and two greedy algorithms -- (i) greedy coordinate descent and (ii) the Frank-Wolfe method. We also present computational guarantees implied by these connections.
Characterization of the power of robust optimization and its applications in electric power systems
Andy Sun
Georgia Institute of Technology, andy.sun@isye.gatech.edu
Inspired by Rob Freund's work on the symmetry of convex sets, we obtain a geometric characterization of the power of robust optimization in both two-stage and multistage decision making frameworks. We will also talk about the recent advances in applying robust optimization to electric power systems operation under high penetration of renewable energy.
Stackelberg games and condition numbers
Fernando Ordonez
Universidad de Chile, fordon@dii.uchile.cl
Recent work has developed Stackelberg game models and their corresponding solution algorithms for applications in security. In this talk I’ll review some recent contributions I’ve participated in on this area of work and present future research directions. Furthermore, I’ll spend time describing the (perhaps fictitious) connection this work on Stackelberg games has with the research on Condition numbers done for my Ph.D. under guidance of Rob Freund.
Variants on the perceptron and von Neumann algorithms
Javier Pena
Carnegie Mellon University, jfp@andrew.cmu.edu
We will recount several recent variants of the perceptron algorithm of Rosenblatt's from the fifties and an algorithm communicated by von Neumann to Dantzig in the forties. These variants are largely inspired by the insightful work of Freund and his collaborators during the last two decades. The new algorithms rely on the tight connections between problem conditioning, problem geometry, and speed of algorithms.
Ill-posedness, Geometry, Complexity and more
Jorge R. Vera
Universidad Catolica de Chile, jvera@ing.puc.cl
The notion of ill-posedness and conditioning in Optimization has been an important conceptual development. Conditions numbers has been shown to explain complexity of both barrier as well as separation oracle algorithms for linear conic optimization, but they also affect sensitivity of problems solutions under data perturbations. In this talk I will review some of the results that have emerged from my collaboration with Robert Freund on these topics, and which are related to the connections between conditioning, complexity of algorithms and also problem geometry. I will also briefly review some of the implications to problem sensitivity and robustness together with some interesting research questions.