Non-negative Polynomials, Sums of Squares & The Moment Problem
This thesis studies polynomial optimization, that is, the problem of minimizing the value of a polynomial over a semi-algebraic set. Such polynomial optimization problems arise in a wide variety of contexts, both in mathematics, and more generally in science and engineering. In the first part of this thesis, we study a polynomial optimization problem which arises when solving the separability problem in Quantum Information Theory. Our approach is via sums of squares decompositions for...[Show more]
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