COMPUTATIONAL EXPERIMENTS WITH A LINEAR APPROXIMATION OF SECOND-ORDER CONE
OPTIMIZATION

In this article, we present and improve a polyhedral approximation of the
second-order cone due to Ben-Tal and Nemirovski. We also discuss several ways
of reducing the size of this approximation. This construction allows us to
approximate second-order cone optimization problems with linear optimization.

We implement this scheme and conduct computational experiments dealing with two
classes of second-order cone problems: the first one involves truss-topology
design and uses a large number of second-order cones with relatively small
dimensions, while the second one models convex quadratic optimization problems
with a single large second-order cone.