报告人：宋晓良 助理研究员 （香港理工大学深圳研究院）

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

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，现为香港理工大学深圳研究院助理研究员。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。

报告时间：2019年11月18日（星期一）下午2：00—4：00

报告地点：科技楼南楼702