嘉宾： 李润泽教授（滨州州立大学）

题目：Global Solutions to Folded Concave Penalized nonconvex Learning

时间：2015年12月18日下午4:00-600

地点： 管理科研大楼1楼EMBA第二教室

摘要：This paper is concerned with solving nonconvex learning problems with folded concave penalty.  Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us  in developing mixed integer linear programming reformulations, which admit finite algorithms that find a provably global optimal solution. We refer to this reformulation-based technique as the mixed integer programming-based global optimization (MIPGO). To our knowledge, this is the first global optimization scheme with a theoretical guarantee for folded concave penalized nonconvex learning with the SCAD penalty (Fan and Li, 2001) and the MCP penalty (Zhang, 2010). Numerical results indicate a significant outperformance of MIPGO over the state-of-the-art solution scheme, local linear approximation, and other alternative solution techniques in literature in terms of solution quality.