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.