Lipschitz continuity of solution multifunctions of the BP-LASSO Problems
报告专家：孟开文 副教授（西南财经大学）
报告时间：2024年11月7日（星期四）下午16：30-17:30
报告地点：数学学院西202报告厅
报告摘要：In this talk we obtain a verifiable sufficient condition for a polyhedral multifunction to be Lipschitz continuous on its domain. We apply this sufficient condition to establish the Lipschitz continuity of the solution multifunction for the BP-LASSO problem with respect to the regularization parameter and the observation parameter under the assumption that the data matrix is of full row rank. In doing so, we show that the solution multifunction is a polyhedral one by expressing its graph as the union of the polyhedral cones constructed by the index sets defined by nonempty faces of the feasible set of the dual problem of the BP-LASSO problem. We demonstrate that the domain of the solution multifunction is partitioned as the union of the projections of the above polyhedral cones onto the parameters space and that the graph of the restriction of the multifunction on each of these projections is convex. In comparing with the existing result of the local Lipschitz continuity of the Lasso problem in the literature where certain linear independence condition was assumed, our condition (i.e., full row rank of data matrix) is very weak and our result (i.e., global Lipschitz continuity) is much more stronger. As corollaries of the global Lipschitz continuity, we show that the single-valuedness and linearity (or piecewise linearity) of the solution multifunction on a particular polyhedral set of the domain are equivalent to certain linear independence conditions of the corresponding columns of the data matrix.
专家简介：孟开文，香港理工大学博士，西南财经大学数学学院副教授，博士生导师。主要从事最优化理论、算法和应用研究，主持国家自然科学基金青年和面上项目各一项。在SIAM J OPT，OR，MP，JMLR,JGO,JCA等期刊上发表学术论文十余篇。
邀请人：方亚平
