A copositive Farkas lemma and minimally exact conic relaxations for robust quadratic optimization with binary and quadratic constraints

摘要

We present a new copositive Farkas lemma for a general conic quadratic system with binary constraints under a convexifiability requirement. By employing this Farkas lemma, we establish that a minimally exact conic programming relaxation holds for a convexifiable robust quadratic optimization problem with binary and quadratic constraints under a commonly used ellipsoidal uncertainty set of robust optimization. We then derive a minimally exact copositive relaxation for a robust binary quadratic program with conic linear constraints where the convexifiability easily holds. (C) 2019 Elsevier B.V. All rights reserved.