Friday,
February 4, 12:00 p.m. PSA 113
Hans Mittelmann
School of Mathematical and Statistical Sciences
Computing Strong Bounds in Combinatorial Optimization
Abstract
As is well-known semidefinite relaxations of discrete optimization problems can
yield excellent bounds on their solutions. We present three examples from our
collaborative research. The first addresses the quadratic assignment problem and
a formulation is developed which yields the strongest lower bounds known for
larger dimensions. Utilizing the latest iterative SDP solver and ideas from
verified computing a realistic problem from communications is solved for
dimensions up to 512.
A strategy based on the Lovasz theta function is generalized to
compute upper bounds on the spherical kissing number utilizing SDP relaxations.
Multiple precision SDP solvers are needed and improvements on known results
for kissing numbers in dimensions up to 23 are obtained. Generalizing ideas
of Lex Schrijver improved upper bounds for general binary codes are obtained
in many cases.
