学术报告
报告题目：A two-phase proximal augmented Lagrangian method for convex quadratic composite conic programming problems
报告人：孙德锋 教授 （新加坡国立大学数学系）
报告时间：2016 年4月 12 日（星期二）上午10:20
报告地点：创新园大厦 A1101
报告校内联系人：张立卫 教授 联系电话：84708351-8118
报告摘要：
In machine learning, finance, statistics, and other areas, numerous interesting problems can be modelled into the form of convex composite quadratic conic programming. In this talk, we use the convex quadratic semidefinite programming (QSDP) problem as an example to introduce a two-phase proximal augmented Lagrangian method, called QSDPNAL, for solving convex composite quadratic conic programming problems with constraints consisting of a large number of linear equality, inequality constraints, a simple convex polyhedral set constraint, and a closed convex cone constraint. As the cornerstone of QSDPNAL, we first introduce the powerful and elegant inexact symmetric Gauss-Seidel (sGS) decomposition technique for solving a convex minimization problem whose objective is the sum of a multi-block quadratic function and a non-smooth function involving only the first block. A first order algorithm which takes advantage of our inexact sGS decomposition technique is adopted in our QSDPNAL-Phase I to generate a reasonably good initial point. Then, in QSDPNAL-Phase II, we design a proximal augmented Lagrangian method (ALM) where the inner sub-problem in each iteration is solved via the inexact accelerated block coordinate descent (ABCD) method, which again relies on our inexact sGS decomposition technique, together with the intelligent incorporation of the semi-smooth Newton-CG algorithm. Moreover, under certain suitable conditions, we are able to analyze the rate of convergence of the proposed algorithm. We further discuss the important numerical issues in the implementation of QSDPNAL. Extensive numerical results for various large scale QSDPs show that our two-phase framework is not only fast but also robust in obtaining accurate solutions. [This talk is based on a joint work with Xudong Li and Kim-Chuan Toh].
报告人简介：
孙德锋，新加坡国立大学数学系教授，现任国际顶级数学期刊Mathematical Programming和SIAM Journal on Optimization编委。曾任Asia-Pacific Journal of Operational Research主编。他于2011年5月，受邀在德国举行的SIAM优化国际会议上作大会报告。他的研究领域为最优化，上世纪90年代中后期在半光滑和光滑化牛顿方法方面取得国际公认的研究成果。本世纪初到现在，他开辟了矩阵优化这一新的学科，建立了非光滑矩阵分析，在矩阵优化的理论、算法及应用方面取得了奠基性的系列成果。
