Talk by Jiawang Nie (UCSD)
Date and Time: Tuesday, November 25, 2008, 12:00 PM in AP&M B412.
Title: Hilbert's 17th Problem and Global Optimization
Abstract:
This lecture will give a brief introduction of Hilbert's 17th
problem: is every nonnegative polynomial a summation of squares of rational
functions? After Artin's affirmative solution, there is a generalization to
Positivstellensatz on the solvability of semialgebraic systems. The
Positivstellensatz can be applied to solve global optimization problems of
polynomial functions. The basic tool is semidefinite programming (SDP), a
very nice convex optimization model.