Computing Strong Bounds in Combinatorial Optimization

Hans Mittelmann

Arizona State University, USA

Monday, June 13, 2016, 11:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

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 all  kissing numbers in dimensions up to 23 are obtained. Finally, generalizing ideas of Lex Schrijver improved upper bounds for general binary codes are obtained in many cases.