Abstract:
The canonical duality is a breakthrough methodological theory, which can be used to model complicated phenomena with a unified solution form to a wide class of non-convex/discrete problems in different fields. It reals an interesting duality pattern in complex systems, which can be used to identify global extrema and to design efficient algorithms for solving challenging problems.

Beginning with a simple quadratic 0-1 programming problem, the speaker will show that by using canonical duality theory, the non-convex integer programming problems can be reformulated as a concave maximization dual problem in continuous space, which can be solved easily for many real-world problems.
Then the speaker will address the canonical duality theory for solving mixed integer programming problem. The speaker will show how the canonical duality theory is precisely developed, why this theory is efficient for solving mixed integer programming problems. Applications will be illustrated by a mixed-integer quadratic fixed charge problem and a general quadratic mixed integer programming problem.