A convex dual programming for the rational minimax approximation and Lawson’s iteration

江苏省应用数学（中国矿业大学）中心系列学术报告

报告题目：A convex dual programming for the rational minimax approximation and Lawson’s iteration

报告人：张雷洪 教授 (苏州大学 数学科学学院)

报告时间：2024年4月21日（周日）上午10:00-11:00

报告地点：数学学院B303

报告摘要：Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan’s sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational approximation algorithms, such as the adaptive Antoulas-Anderson (AAA), AAA-Lawson, and the rational Krylov fitting (RKFIT) method, perform highly efficiently, but the computed rational approximants may be near-best. In this paper, we propose a convex programming approach, the solution of which is guaranteed to be the rational minimax approximation under Ruttan’s sufficient condition. Furthermore, we present a new version of Lawson’s iteration for solving this convex programming problem. The computed solution can be easily verified as the rational minimax approximant. We show that this updated version of Lawson’s iteration converges monotonically with respect to the objective function of the convex programming.  It is an effective competitive approach for the rational minimax problem, compared to the highly efficient AAA, AAA-Lawson, and the stabilized Sanathanan-Koerner iteration.

报告人简介：张雷洪，2008年博士毕业于香港浸会大学，现为苏州大学数学科学学院教授。从事最优化理论与计算，数值线性代数，数值逼近，数据挖掘等领域的研究。曾赴美国北卡罗来纳州立大学、美国德克萨斯大学阿灵顿分校等进行访问。获中国数学会计算数学分会的第四届“应用数值代数奖”， 2018 年和 2019 年两届“世界华人数学家联盟最佳论文奖-若琳奖”，2019 年上海市自然科学三等奖(第一完成人)。 成果发表在包括SIAM系列杂志,及《Math. Progam.》、《Math. Comp.》、《Numer. Math.》、《IEEE Trans. Pattern Anal. Mach. Intell.》等。主持多项国家自科项目,参与国家重大研究计划。目前任SCI杂志《Operators and Matrices》，ESCI期刊《Numerical Algebra, Control and Optimization》，《计算数学》编委等。