In this talk we first give a brief introduction to Khintchine-type inequalities, which are inequalities that bound the moments of the norm of a certain sum of independent Banach space-valued random variables. Then, we will discuss how these inequalities can be used to obtain the best known bounds for several optimization problems, including the approximation of a class of quadratic optimization problems with orthogonality constraints, the design of so-called safe tractable approximations for chance constrained linear matrix inequality systems, and the design of efficient sampling procedures for certain stochastic optimization problems.
Anthony Man-Cho So received his BSE degree in Computer Science from Princeton University in 2000 with minors in Applied and Computational Mathematics, Engineering and Management Systems, and German Language and Culture. He then received his MSc degree in Computer Science in 2002, and his PhD degree in Computer Science with a PhD minor in Mathematics in 2007, all from Stanford University. Dr. So joined the Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong in 2007, where he is currently an assistant professor. His current research focuses on the interplay between optimization theory and various areas of algorithm design, such as computational geometry, stochastic optimization, combinatorial optimization, and algorithmic game theory.