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Center for Nonlinear Studies |
A brief history of Hilbert's 17-th problem and its impact on Real Algebraic Geometry will be given. A powerful correspondence between the spectral theorem for normal operators, the structure of positive polynomials on semi-algebraic sets and moment problems will lead to a new perspective on non-linear polynomial optimization problems. Recent developments in this field, as well as ramifications of the main results into the free *-algebra setting or to optimization of measurable functions will be outlined. Some applications to optimal control theory will be sketched.
Host: Razvan Teodorescu