报 告 人：李润泽
报告地点：数学与统计学院五楼科学报告厅（501室）
报告时间：2015年10月19日星期一10:00-11:00
主讲人简介：
Academic Positions: Distinguished Professor, Penn State University, 2012 – Full Professor, Penn State University, 2008 – 2012 Associate Professor, Penn State University, 2005-2008 Assistant Professor, Penn State University, 2000-2005 Honors and Awards: NSF Career Award, 2004 Fellow, Institute of Mathematical Statistics Fellow, American Statistical Association The United Nations World Meteorological Organization Gerbier-Mumm International Award for 2012 Selection criterion for this award
报告摘要：
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.
