**A Modified Frank-Wolfe Algorithm for Computing Minimum-Area**

**Enclosing Ellipsoidal Cylinders: Theory and Algorithms**

*Selin** Damla Ahipasaoglu and Michael J. Todd*

ABSTRACT: Given an arbitrary set in
the Euclidean space, we are

interested in finding an ellipsoidal cylinder,
centered at the origin, such that

its intersection with a certain
subspace has minimum area. This problem is

referred to as the Minimum-Area Enclosing
Ellipsoidal Cylinder (MAEC)

problem. We show that MAEC and its dual can be written as convex

problems, and present a Frank-Wolfe type
algorithm with away steps. We discuss

global and local convergence properties of
the algorithm and present some

computational results.