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Cluster :  Global Optimization

Session Information  : Thursday Jul 16, 17:30 - 19:00

Title:  Synergies Between Optimization and Robust Control
Chair: Venkat Chandrasekaran,Caltech, 1200 E. California Blvd, MC 305-16, Pasadena CA 91125, United States of America, venkatc@caltech.edu

Abstract Details

Title: Robust to Dynamics Optimization (RDO)
 Presenting Author: Amir Ali Ahmadi,Princeton University, a_a_a@princeton.edu
 Co-Author: Oktay Gunluk,IBM Research, 1101 Kitchawan Road, Yorktown Heights, United States of America, gunluk@us.ibm.com
 
Abstract: We introduce a new type of robust optimization problems that we call "robust to dynamics optimization" (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. We initiate an algorithmic study of RDO and demonstrate tractability of some important cases.
  
Title: Regularization for Design
 Presenting Author: Nikolai Matni,California Institute of Technology, 1200 E California Blvd, MC 305-16, Pasadena CA 91125, United States of America, nmatni@caltech.edu
 Co-Author: Venkat Chandrasekaran,Caltech, 1200 E. California Blvd, MC 305-16, Pasadena CA 91125, United States of America, venkatc@caltech.edu
 
Abstract: When designing controllers for large-scale systems, designing the controller architecture, i.e., placing sensors and actuators as well as the communication links between them, is as important as the design of the control laws themselves. We show that the architecture design task can be framed as one of seeking structured solutions to linear inverse problems. We use this observation to formulate the Regularization for Design framework, in which we augment variational formulations of controller synthesis problems with convex penalty functions that induce a desired controller architecture. We further show that the resulting convex optimization problems identify optimally structured controllers under a signal-to-noise ratio type condition.
  
Title: Analysis and Design of Optimization Algorithms using Robust Control
 Presenting Author: Benjamin Recht,UC Berkeley, 465 Soda Hall, MC 1776, Berkeley CA 94720, United States of America, brecht@berkeley.edu
 
Abstract: I will present a method to analyze and design optimization algorithms built on the framework of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide conditions for ensuring the stability of complicated interconnected systems and can be checked via semidefinite programming. I will discuss how to adapt IQC theory to study optimization algorithms, deriving upper bounds on convergence rates for many popular optimization methods. I will close with a discussion of how these techniques can be used to search for optimization algorithms with desired performance characteristics, establishing a new methodology for algorithm design. This is joint work with Laurent Lessard and Andrew Packard.