大连理工大学数学科学学院
通知与公告

【香港理工大学】An Efficient Duality-based Numerical Method for Sparse Optimal Control Problems

2019年05月15日 09:51  点击:[]

报告题目An Efficient Duality-based Numerical Method for Sparse Optimal Control Problems

 

报告人:  宋晓良 香港理工大学博士后

 

报告时间516号(周四)下午1530-1615

 

报告地点:创新园大厦A1101

 

报告校内联系人:雷逢春  教授   联系电话:84708360

 

报告摘要In this paper, elliptic optimal control problems involving the $L^1$-control cost ($L^1$-EOCP) is considered. To numerically discretize $L^1$-EOCP, the standard piecewise linear finite element is employed. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discrete $L^1$-norm does not have a decoupled form. A common approach to overcome this difficulty is employing a nodal quadrature formula to approximately discretize the $L^1$-norm. It is clear that this technique will incur an additional error. To avoid the additional error, solving $L^1$-EOCP via its dual, which can be reformulated as a multi-block unconstrained convex composite minimization problem, is considered. Motivated by the success of the accelerated block coordinate descent (ABCD) method for solving large scale convex minimization problems in finite dimensional space, we consider extending this method to $L^1$-EOCP. Hence, an efficient inexact ABCD method is introduced for solving $L^1$-EOCP. The design of this method combines an inexact 2-block majorized ABCD and the recent advances in the inexact symmetric Gauss-Seidel (sGS) technique for solving a multi-block convex composite quadratic programming whose objective contains a nonsmooth term involving only the first block. The proposed algorithm (called sGS-imABCD) is illustrated at two numerical examples. Numerical results not only confirm the finite element error estimates, but also show that our proposed algorithm is more efficient than (a) the ihADMM (inexact heterogeneous alternating direction method of multipliers), (b) the APG (accelerated proximal gradient) method.

 

报告人简介:

宋晓良,2018年博士毕业于大连理工大学,2015.09-2017.02在新加坡国立大学联合培养,现为香港理工大学应用数学系博士后。宋晓良博士的研究方向为数值优化和最优控制,主要研究内容为主PDE约束优化问题的数值离散和优化算法的研究。目前已发表学术论文11篇。

 

    欢迎广大师生踊跃参加!



数学科学学院

2019年5月15日

上一条:2019中科院华罗庚班数学思想方法系列讲座 (八)机器学习中的优化模型与算法 下一条:【特拉华州立大学】The Haar Wavelet Analysis of Matrices and its Applications

关闭