Removing redundant quadratic constraints

Abstract

Determining whether an ellipsoid contains the intersection of many concentric ellipsoids is an NP-hard problem. In this paper, we study various convex relaxations of this problem, namely two semidefinite relaxations and a second-order cone relaxation. We establish some links between these relaxations and perform extensive numerical testings to verify their exactness, their computational load and their stability. As an application of this problem, we study an issue emerging from an aircraft wing design problem: how can we simplify the description of a feasible loads region? © 2010 Springer-Verlag.