The Complexity of Computing KKT Solutions of Quadratic Programs

26^th March 2024, 13:00 Ashton Lecture Theatre
Dr. Alexandros Hollender
All Souls College, Oxford

Abstract

It is well known that solving a (non-convex) quadratic program is NP-hard. We show that the problem remains hard even if we are only looking for a Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove that computing a KKT point of a quadratic polynomial over the domain [0,1]^n is complete for the class CLS = PPAD ∩ PLS.

Based on joint work with John Fearnley, Paul W. Goldberg, and Rahul Savani.