Chen Chen

Columbia University

Spatial Branch-and-Cut for Polynomial Optimization

A polynomial optimization problem has an objective function and constraints described by polynomials. Although the problem is computationally challenging (binary integer programming is a special case), polynomial functions provide tremendous modeling flexibility that can be used to capture physical phenomena, uncertainty (e.g. correlated chance constraints), and competition (e.g. bilevel optimization). This talk will focus on an application of scheduling electric generation while modeling steady-state power flows across a network. We will use the branch-and-cut framework for negotiating the trade-off between time, space, and solution quality. The talk will conclude with recent work on strengthening convex relaxations for polynomial optimization by means of convex forbidden zones or S-free sets.