Plenary Lecture

Polynomial Optimization via Sums
of Squares Relaxations

Professor Mihai Putinar
Mathematics Department
University of California at Santa Barbara
CA 93117, USA
http://www.math.ucsb.edu/~mputinar

Abstract: The lecture will focus on the rapidly developing area of polynomial optimization via sums of squares methods. A functional analytic proof of a key Positivstellensatz in real algebraic geometry will be discussed, in conjunction with the method of moments approach to non-linear optimization. The case of hermitian squares or non-commuting variables will occupy a second part of the talk.

Brief Biography of the Speaker:
Mihai Putinar gained his M.S. in 1980 and his Ph.D. in 1984 at the University of Bucharest, Romania. During the past 20 years, he was tenured in several European and American Universities. He is a currently a professor in the Mathematics Department of the University of California at Santa Barbara. Prof. Putinar has been invited to present lectures in a number of international scientific conferences, and he has co-organized several scientific workshops and conferences. He is a member of the Editorial Board of Journal of Operator Theory (Theta Foundation), Integral Equations and Operator Theory (Birkhauser), Journal of Mathematical Analysis and Applications (Elsevier), Operator Theory: Advances and Applications (Birkhauser), Complex Analysis and Operator Theory (Birkhauser), The Open Mathematics Journal, The Open Applied Mathematics Journal, (Bentham Science Publishers). He is the author of more than 100 research articles and several specialized monographs.
His research areas are:
Operator theory: multivariable spectral theory, hyponormal operators, perturbation theory, local spectral theory;
Complex analytic geometry: the cohomology of analytic sheaves, holomorphic vector bundles on compact complex manifolds, the theory of Stein spaces;
Analysis: Moment problems, quadrature formulas, rational approximation.