Fall 2010, Thursdays, Milner 216, 4:00-4:50 PM

Date: October 14

"  Optimizing n-variate (n+k)-nomials for Small k "
 Prof. Maurice Rojas  


Maximizing, or minimizing, a polynomial function is a basic problem in nonlinear optimization and is ubiquitous in engineering applications. We reveal a setting where dramatically faster algorithms are possible: sparse polynomials. In particular, you'll learn how to efficiently optimize any polynomial in n variables having n+2 or fewer monomial terms. The algorithms ultimately boil down to some cute diagrams originally discovered by Viro, as well as clever iterations for the log and exp functions. No background in algebraic geometry is assumed.
This is joint work with Philippe P. Pebay and David C. Thompson, of Sandia National Laboratories.