| Research in this project focuses on the interplay between semidefinite programming and combinatorial optimization. One of the main objectives is the design of strong and efficient approximations to hard problems, such as combinatorial optimization problems and integer and polynomial programming problems (i.e., minimizing a polynomial function over a real semi-algebraic set defined by polynomial equations and inequalities). The methods use combinatorial, geometric, and algebraic tools; e.g., from real algebraic geometry about positive polynomials and sums of squares of polynomials and the dual theory of moments, representation and invariant theory for exploiting symmetry, etc. |
