报告地点：行健楼-526
邀请人：姜波副教授
摘要：In this talk, we study the local variational geometry of the optimal solution set of the trust region subproblem (TRS), which minimizes a general, possibly nonconvex, quadratic function over the unit ball. Specifically, we demonstrate that a Hölderian error bound holds globally for the TRS with modulus 1/4 and the Kurdyka-Łojasiewicz (KL) inequality holds locally for the TRS with a KL exponent 3/4 at any optimal solution. We further prove that unless in a special case, the Hölderian error bound modulus, as well as the KL exponent, is 1/2. Finally, based on the obtained KL property, we further show that the projected gradient methods studied in [A. Beck and Y. Vaisbourd, SIAM J. Optim., 28 (2018), pp. 1951--1967] for solving the TRS achieve a sublinear or even linear rate of convergence.
报告人简介：江如俊，复旦大学大数据*女王调教-女王调教视频-女王 调教小说副教授。 研究方向主要包括大规模优化算法和理论分析，二次规划，混合整数规划及其在运筹学、机器学习和金融工程领域的应用。在运筹优化国际期刊《Mathematical Programming》，《SIAM Journal on Optimization》，《INFORMS Journal on Computing》等发表多篇论文。入选2018年度上海市青年科技英才扬帆计划。现为多个国际运筹优化期刊匿名审稿人及美国数学学会旗下Mathematical Reviews的评论员。