報告人：澳大利亞聯邦國立大學教授阮寧

報告題目：對偶理論——一個求解混合整數規劃問題的同一方法及應用

（Canonical Duality Theory: A Unified Methodological Theory for Solving Mixed Integer Programming Problems with Applications)

報告時間:2015-1月8日? 18:00

報告地點:泰山樓517A

報告摘要：

Canonical Duality Theory: A Unified Methodological Theory for Solving Mixed Integer Programming Problems with Applications

Ning Ruan

Faculty of Science and Technology, Federation University Australia, Australia

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.