Abstract
Distributed convex optimization algorithms employ a variety
of methods for achieving exact convergence to the global optimum. All
such methods have their drawbacks. For example, some methods use a
specific initialization onto a particular invariant subspace, which
means the resulting algorithms are unable to recover from faults or
disturbances that perturb their dynamics from this subspace. We
present a new class of control-inspired algorithms that have none of
the existing drawbacks, but that do have a drawback of their own: all
nodes have states that grow linearly in time even as their outputs
converge to the global optimum. For applications such as swarm
robotics, permitting this mild internal instability may be worth
avoiding the various drawbacks of existing methods. We apply our
methods to solve distributed versions of some convex optimization
problems, including support vector machines, matrix completion, and
graphical lasso.
Biography
Randy A. Freeman received a Ph.D. in Electrical Engineering from
the University of California at Santa Barbara in 1995, after having
received B.S and M.S. degrees in EE from Cornell University and the
University of Illinois at Urbana-Champaign (respectively). Since then
he has been a faculty member at Northwestern University (Evanston,
Illinois), where he is currently a Professor of Electrical and
Computer Engineering. He is a recipient of the National Science
Foundation CAREER Award, as well as best paper awards from the Asian
Journal of Control and the IEEE Control Systems Magazine. His
research interests include nonlinear system theory, nonlinear control,
robust control, optimal control, and distributed control and
estimation.
