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博学堂讲座
Linear convergence of descent methods for lower-order regularization problems (第229讲)
浏览量：1304    发布时间：2017-03-20 14:42:58

报告题目:Linear convergence of descent methods for lower-order regularization problems

报告人：李冲 教授

报告时间：下午4点

报告地点：广B106

题目：Linear convergence of descent methods for lower-order
regularization problems
时间: 3月23日(周四)  16:00   
地点：广B106
报告人：李冲 教授
摘要： The lower-order regularization problem (i.e., the ℓp regularization problem
(0 < p < 1)) has been widely studied for finding sparse solutions of linear
inverse problems and gained successful applications in various mathematics
and applied science fields. Several descent methods have been proposed and
investigated for solving the ℓp regularization problem. However, a complete
optimality condition of local minima and the convergence rates of the descent
methods for the ℓp regularization problem have not been well investigated
yet. To remedy this gap, in this talk, we will first provide a necessary and
sufficient optimality condition for local minima and to show the property
of strict local minima of order 2 for the ℓp regularization problem. This
not only shows the advantage of applying ℓp regularization to induce sparse
solutions, but also provides a tool for the linear convergence study of the descent
methods. Then we will establish the linear convergence of the descent
methods under the simple assumption that the limiting point of iterates is
a local minimum of the ℓp regularization problem. Applying this abstract
convergence theorem, we will also study the linear convergence of the wellknown
proximal gradient algorithm, as well as the inexact proximal gradient
algorithm.
This work is joint work with Dr. Yaohua Hu (Shenzhen University), Dr.
Kaiwen Meng (Southwest Jiaotong University) and Prof. Xiaoqi Yang (Hong
Kong Polytechnic University). 
 
报告人简介：
李冲，浙江大学数学系教授、博士生导师。主要从事非线性逼近理论、非线性优化理论、科学计算等领域的研究。应邀多次访问香港中文大学、香港科技大学、台湾中山大学、澳大利亚新南威尔士大学、西班牙Sevillia大学、在国际顶级期刊Math. Program、SIAM J. Optim、SIAM J.Control Optim 、IMA J. Numer. Anal.和著名期刊J. London. Math. Soc.、Nonlinear Anal.、J. Approx. Theory、J. Complexity等上发表SCI学术论文150余篇，出版专著1部。主持承担完成国家自然科学基金面上项目10项、首届教育部新世纪优秀人才计划项目1项、省部级基金项目5项。1992年被评为原商业部有突出贡献的中青年专家，享受政府特殊津贴。1995年获浙江省青少年英才奖。1998年入选为江苏省“青蓝工程”青年骨干教师。2002年获教育部优秀骨干教师。
 
博学堂讲座
Linear convergence of descent methods for lower-order regularization problems (第229讲)
浏览量：1304    发布时间：2017-03-20 14:42:58

报告题目:Linear convergence of descent methods for lower-order regularization problems

报告人：李冲 教授

报告时间：下午4点

报告地点：广B106

题目：Linear convergence of descent methods for lower-order
regularization problems
时间: 3月23日(周四)  16:00   
地点：广B106
报告人：李冲 教授
摘要： The lower-order regularization problem (i.e., the ℓp regularization problem
(0 < p < 1)) has been widely studied for finding sparse solutions of linear
inverse problems and gained successful applications in various mathematics
and applied science fields. Several descent methods have been proposed and
investigated for solving the ℓp regularization problem. However, a complete
optimality condition of local minima and the convergence rates of the descent
methods for the ℓp regularization problem have not been well investigated
yet. To remedy this gap, in this talk, we will first provide a necessary and
sufficient optimality condition for local minima and to show the property
of strict local minima of order 2 for the ℓp regularization problem. This
not only shows the advantage of applying ℓp regularization to induce sparse
solutions, but also provides a tool for the linear convergence study of the descent
methods. Then we will establish the linear convergence of the descent
methods under the simple assumption that the limiting point of iterates is
a local minimum of the ℓp regularization problem. Applying this abstract
convergence theorem, we will also study the linear convergence of the wellknown
proximal gradient algorithm, as well as the inexact proximal gradient
algorithm.
This work is joint work with Dr. Yaohua Hu (Shenzhen University), Dr.
Kaiwen Meng (Southwest Jiaotong University) and Prof. Xiaoqi Yang (Hong
Kong Polytechnic University). 
 
报告人简介：
李冲，浙江大学数学系教授、博士生导师。主要从事非线性逼近理论、非线性优化理论、科学计算等领域的研究。应邀多次访问香港中文大学、香港科技大学、台湾中山大学、澳大利亚新南威尔士大学、西班牙Sevillia大学、在国际顶级期刊Math. Program、SIAM J. Optim、SIAM J.Control Optim 、IMA J. Numer. Anal.和著名期刊J. London. Math. Soc.、Nonlinear Anal.、J. Approx. Theory、J. Complexity等上发表SCI学术论文150余篇，出版专著1部。主持承担完成国家自然科学基金面上项目10项、首届教育部新世纪优秀人才计划项目1项、省部级基金项目5项。1992年被评为原商业部有突出贡献的中青年专家，享受政府特殊津贴。1995年获浙江省青少年英才奖。1998年入选为江苏省“青蓝工程”青年骨干教师。2002年获教育部优秀骨干教师。