TITLE: Recent results on polynomial optimization problems

ABSTRACT:

Polynomial optimization problems, as the name suggests, are optimization problem where the objective function as well as the constraints are described by polynomials.  Such problems have acquired increased interest to some degree because of applications in engineering and science, where constraints arise because of physics, and also because of increased theoretical understanding.  In this talk I will focus on two topics where I am working, the CDT (Celis Dennis Tapia) problem, which concerns the solution of a system of quadratic inequalities over R^n, and mixed-integer polynomial optimization problems over graphs with structural sparsity, i.e. low treewidth.  We will describe our results, but also we will discuss how these problems relate to classical problems in various branches of mathematics.

Bio:

Daniel Bienstock is a professor at the departments of Industrial Engineering and Operations Research, and Applied Physics and Applied Mathematics, Columbia University, where he has been since 1989.   He received the PhD from MIT in Operations Research. His research focuses on discrete and nonconvex optimization, from both a theoretical and a computational standpoint, and applications, such as the mathematics of power grids.  He was plenary speaker at the 2005 SIAM Conference on Optimization, semi-plenary speaker at the 2006 ISMP meeting, became an INFORMS fellow in 2013, and is editor-in-chief of Mathematical Programming C.