8:45 AM / Salon A/B

Wednesday, May 22
## IP6

Convex Analysis and Applications

Convex analysis, like elementary calculus, has two apparently divergent attractions. For the skeptical practitioner it provides a powerful toolkit of straightforward calculus rules for convex optimization; for the intrigued theorist these same rules revolve around elegant central ideas. I will discuss three of these ideas: the existence of subgradients, Fenchel biconjugation, and the compactness of level sets. Each idea I will apply to an interesting optimization problem: matrix balancing, semidefinite programming, and maximum entropy density estimation. For each problem I will try to demonstrate how a simple theoretical idea enhances our understanding and
algorithms.
**Adrian S. Lewis**

University of Waterloo

Canada

*MEM, 3/11/96*