Title: Validated Numerical Optimization

Rigorous global optimization algorithms use interval arithmetic and automatic differentiation. We outline the building blocks of a global optimization algorithm and comment on how interval methods can act as a super sensitivity analysis and aid in finding regions where system outputs are relatively insensitive to variations in system inputs and parameters. We describe several industrial applications of interval techniques for global optimization, including problems from Sun Microsystems (software development), MacNeal-Schwindler (finite element), Bank One (portfolio management), Swiss National Bank (currency trading), GE Medical Systems (control of NMR signals), and Genome Thereputics. Interval methods have some possibilities and some limitations for handling optimization with uncertainties.
This talk should be accessible to a third semester calculus student and beyond. It should be interesting to researchers using optimization techniques in scientific or engineering applications.
Short Bio:
Dr. George Corliss, Marquette University, Milwaukee WI, holds faculty appointments in Engineering, in Arts & Sciences, and in Business. He is a researcher in scientific computation, especially in interval techniques and automatic differentiation. He is a veteran teacher of computer science and engineering topics, especially their applications, with considerable industrial mathematics and computing experience. He directs a masters program catering to working IT professionals.