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：5月16号（周四）下午15：30-16：15
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437ccm必赢国际首页欢迎您，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。
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2019年5月15日
