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2020年12月10日罗自炎教授线上学术报告
上传时间:2020-12-02 作者: 浏览次数:10

报告标题: A Lagrange-Newton Algorithm for Sparse Nonlinear Programming
报告人:罗自炎(北京交通大学副教授)
报告摘要:  The sparse nonlinear programming (SNP) problem has wide applications in signal and image processing, machine learning, pattern recognition, finance and management, etc. However, the computational challenge posed by SNP has not yet been well resolved due to the nonconvex and discontinuous $\ell_0$-norm involved. In this paper, we resolve this numerical challenge by developing a fast Newton-type algorithm. As a theoretical cornerstone, we establish a first-order optimality condition for SNP based on the concept of strong $\beta$-Lagrangian stationarity via the Lagrangian function, and reformulate it as a system of nonlinear equations called the Lagrangian equations. The nonsingularity of the corresponding Jacobian is discussed, based on which the Lagrange-Newton algorithm (LNA) is then proposed. Under mild conditions, we establish the local quadratic convergence rate and the iterative complexity estimation of LNA. To further demonstrate the efficiency and superiority of our proposed algorithm, we apply LNA to solve three specific application problems arising from compressed sensing, sparse portfolio selection and sparse principal component analysis, in which significant benefits accrue from the restricted Newton step in LNA.


报告时间:20201210日(周四)下午1330-1430
报告地点:腾讯会议(会议ID354221404


报告人简介:罗自炎,女,北京交通大学4166金沙手机官网副教授、博士生导师。2010年获北京交通大学4166金沙手机官网运筹学与控制论专业博士学位,美国Stanford大学管理与科学工程系、新加坡国立大学、英国南安普顿大学访问学者、香港理工大学应用数学系研究助理。主要从事大规模统计优化算法设计、稀疏与低秩优化、张量分析与张量理论等方面的研究。共发表SCI检索期刊论文30余篇,其中ESI高被引论文2篇。撰写英文专著1部,由国际著名SIAM出版社于20174月出版,编写中文著作《半定规划》, 已被国内多所高校的优化专业选为研究生教材。主持国家自然科学基金面上项目、国家自然科学基金重点项目子课题、国家自然科学基金青年基金项目、北京市自然科学基金重点项目各1项。2016年在北京运筹学年会上做大会特邀报告,2017年在第十一届全国数学规划学术会议上做青年专题报告,2020年获中国运筹学会青年科技奖提名奖。

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