Tuesday, 13:15 - 13:40 h, Room: H 2036

 

Luis Zuluaga
Positive polynomials on unbounded domains

Coauthors: Javier F. Peña, Juan C. Vera

 

Abstract:
Certificates of non-negativity are fundamental tools in optimization. A "certificate'' is generally understood as an expression that makes the non-negativity of the function in question evident. Recently, sum-of-squares certificates of non-negativity for polynomials have been used to obtain powerful numerical techniques for solving polynomial optimization problems; in particular, for mixed integer programs, and non-convex binary programs. We present a new certificate of non-negativity for polynomials over the intersection of a closed set S and the zero set of a given polynomial h(x). The certificate is written in terms of the set of non-negative polynomials over S and the ideal generated by h(x). Our certificate of non-negativity yields a copositive programming reformulation for a very general class of polynomial optimization problems.

 

Talk 1 of the invited session Tue.2.H 2036
"Advances in convex optimization" [...]
Cluster 4
"Conic programming" [...]

 

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