In recent years, the theory of sums of squares emerged as a very useful tool for polynomial optimization. The development of approximation methods based on classic Positivstellensatzes, raised a number of interesting theoretical questions that relate to very classic subjects of algebraic geometry. In this talk we will give a brief introduction to the theory of positivity and sums of squares, show how it relates to polynomial optimization and present some of the algebraic problems that are naturally raised.
|