Title
A Comparison of Convex Relaxations of Optimization Problems with Hard Cardinality Constraints
Abstract
Sparsity plays a vital role in a wide range of applications such as machine learning, data science, image processing, portfolio management, and sparse regression due to the interpretability, robustness, and ease of implementation of sparse solutions. As such, optimization problems with cardinality constraints arise in a plethora of applications such as interpretable machine learning, portfolio optimization, and principal component analysis.
In this talk, we consider alternative formulations of the NP-hard class of optimization problems with hard cardinality constraints. We introduce various polyhedral and convex conic relaxations of such formulations. We compare the resulting convex relaxations in terms of their strength and computational cost. We present preliminary computational results.
Bio
E. Alper Yildirim is a Reader at the School of Mathematics at the University of Edinburgh. Prior to joining the University of Edinburgh, he held faculty positions at Stony Brook University (USA), Bilkent University (Turkey), and Koc University (Turkey). His research interests are in mathematical optimization and applications of optimization in different fields. He is particularly interested in convex conic optimization and various convex relaxations of nonconvex optimization problems. He currently serves on the Editorial Boards of Journal of Global Optimization, Optimization Methods and Software, Optimization Letters, EURO Journal on Computational Optimization, and Journal of Optimization Theory and
Applications.