CULLEN COLLEGE OF ENGINEERING

University of Houston Cullen College of Engineering

Department Event / Seminar

[IE] Perspectives on Integer Programming in Sparse Optimization

Date: 

Friday, November 2, 2018 - 1:00pm to 2:00pm

Location: 

D3 W122, College of Engineering, University of Houston

Algorithms to solve mixed integer linear programs have made incredible progress in the past 20 years. Key to these advances has been a mathematical analysis of the structure of the set of feasible solutions. We argue that a similar analysis is required in the case of mixed integer quadratic programs, like those that arise in sparse optimization in machine learning. One such analysis leads to the so-called perspective relaxation, which significantly improves solution performance on separable instances. Extensions of the perspective reform-ulation can lead to algorithms that are equivalent to some of the most popular, modern, sparsity-inducing non-convex regularizations in variable selection, such as the minimax concave penalty.