Strong nonnegativity and sums of squares on real varieties

12/06/2011 - 12:15pm
12/06/2011 - 1:10pm
Mohamed Omar (California Institute of Technology)

The success of linear optimization has been afforded by our deep understanding of the geometry underlying convex polyhedra. In a similar light, polynomial optimization has benefitted from recent advances in the study of convex hulls of algebraic varieties. Motivated by scheme theory, we introduce strong nonnegativity, a construction that implicitly carries both geometric and algebraic properties of nonnegativity on a variety. In particular, we will explore the role strong nonnegativity plays in advancing polynomial optimization. This is joint work with Brian Osserman.

Millikan 134 (Pomona College)