Approximation of Positive Polynomials by Sums of Squares

Saturday, January 20, 2007 - 11:00am - 11:50am
EE/CS 3-180
Salma Kuhlmann (University of Saskatchewan)
Approximation of positive polynomials by sums of squares has important
applications to polynomial optimisation. In this talk, I will survey
the main recent results achieved on that topic:
I will consider positive (respectively, non-negative) polynomials on
compact (respectively, unbounded) semi-algebraic sets. I will discuss
representations in the associated preorderings (respectively, linear
representations in the associated quadratic module). The
representation often depends on
the dimension of the semi-algebraic set; I will present stronger results
in the low dimensional case. I will also highlight special representations
when the positive polynomials under consideration are sparse (that is,
satisfy some separation and overlap conditions on the variables appearing
in the monomials).
MSC Code: