Title: Linear Programming Approaches to Polynomial Optimization

Abstract:

Modern problems arising in many domains are driving a need for more capable, state-of-the-art optimization tools. A sharp focus on performance and accuracy has appeared, for example, in science and engineering applications. In particular, we have seen a growth in studies related to Polynomial Optimization: a field with beautiful and deep theory, offering flexibility for modeling and high impact in diverse areas. In this talk we will explore theoretical and practical LP-based techniques for polynomial optimization problems. Motivated by the AC-OPF problem in Power Systems, we will review how "tree-like" sparsity can be exploited as a tool for analysis of the fundamental complexity of the problem, by showing LP formulations that can efficiently approximate such sparse problems. In addition, we will show a computationally practical approach for constructing such approximations on-the-fly. Our methods rely on the maturity of current LP technology; we believe these contributions are important for the development of manageable approaches to general polynomial optimization problems.

Bio: Gonzalo Muñoz is a PhD Candidate of the Industrial Engineering and Operations Research Department at Columbia University. His research interests fit in the category of Non-Linear Mixed-Integer Optimization, including both theoretical perspectives and implementation of efficient algorithms to address this type of problems. Recently, he has worked on efficient LP approximations to sparse polynomial problems. The main applications of these methodologies are drawn from Power Grid operations and Mining scheduling problems.