OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

7th Simon Stevin Lecture on Optimization in Engineering

"Nonsmooth, Nonconvex Optimization, with Applications in Control" Slides
Michael Overton
Professor of Computer Science and Mathematics (New York University)
http://www.cs.nyu.edu/overton/



Abstract:

There are many algorithms for minimization when the objective function is differentiable, convex, or has some other known structure, but few options when none of the above hold. We describe two simple algorithmic approaches for minimization of nonsmooth, nonconvex objectives: Gradient Sampling (a new method that, although computationally intensive, has a nice convergence theory, which we will outline), and BFGS (a new look at an old method, for which we have no theoretical results, but some interesting empirical observations).
Both methods require the user to provide a routine that computes the function value and, if it exists, the gradient at a given point, the idea being that the function is virtually never evaluated at a point where it is not differentiable, even though it is typically not differentiable at local optimizers.
Applications abound in control. Of particular interest to us is H-infinity fixed-order controller design. We briefly describe our code HIFOO: H-Infinity Fixed-Order Optimization, which is built on HANSO: Hybrid Algorithm for Non-Smooth Optimization.

Bibliographical Information:

Michael L. Overton received his BSc from UBC in 1974, along with the Governor General’s Gold Medal for Arts and Sciences. He received the MS and PhD degrees in Computer Science from Stanford University. He is currently Professor of Computer Science and Mathematics at the Courant Institute of Mathematical Sciences, New York University. Michael Overton is an elected member of the Board of Trustees of SIAM (Society for Industrial and Applied Mathematics) and has also served on the SIAM Council. He is a member of the Council of FoCM (Foundations of Computational Mathematics) and of the Board of Directors of the Canadian Mathematical Society. He serves on the editorial boards of SIAM Journal on Optimization (for which he was Editor-in-Chief from 1995-1999), SIAM Journal on Matrix Analysis and Applications, the IMA Journal on Numerical Analysis, and SIAM Review. His research interests are at the interface of optimization and linear algebra, especially nonsmooth optimization problems involving eigenvalues, with applications to many dierent subjects including robust control, structural analysis, combinatorial optimization and convex analysis. He is author of "Numerical Computing with IEEE Floating Point Arithmetic" (SIAM, 2001).

About the Lecture Series:

The "Simon Stevin Lecture Series on Optimization in Engineering" is set up in order to promote optimization in engineering. For this aim, every quarter of the year an outstanding international scholar is invited to report on latest progress in the development of optimization algorithms and their applications in engineering.
Simon Stevin (1548-1620) was a Flemish mathematician and engineer. Among other, he helped to advance the use of decimal fractions, was the first to explain the tides by the attraction of the moon, and discovered the hydrostatic paradox. He made numerous inventions, among them a wind propelled carriage with sails, the "land yacht", which once impressed Prince Maurice of Orange as it moved faster than horses, in around 1600 on the beach between Scheveningen and Petten. Simon Stevin was fond of promoting the use of science in daily life and in craftmanship, and translated various mathematical terms into dutch. Among other, he introduced the dutch word for mathematics, "wiskunde".

Directly after this Simon Stevin Lecture, a little reception will be given at 18:00 in the salons of Arenberg Castle, to which all attendants of the lecture are most warmly welcome!

***** REGISTRATION ENCOURAGED *****
Please send an e-mail with the subject "STEVIN" to Ida.Tassens@esat.kuleuven.be if you intend to participate in the event. No obligation, just to help us getting an idea how many people plan to come.

This Stevin lecture is co-sponsored by ICCoS (Identification and Control of Complex Systems), a Scientific Research Network of the Research Foundation - Flanders (FWO-Vlaanderen).