数苑讲座之十一：Constraint Dissolving Approaches for a Class of Riemannian Optimization Problems

发布时间：2023-04-24 作者：77779193永利集团浏览次数：

Speaker	刘歆教授	DateTime	2023年4月24日（周一）10:00-11:30
Place	6号楼6401报告厅	Abstract	We propose constraint dissolving approaches for optimization problems over a class of Riemannian manifolds. In these proposed approaches, solving a Riemannian optimization problem is transferred into the unconstrained minimization of a constraint dissolving function named CDF. Different from existing exact penalty functions, the exact gradient and Hessian of CDF are easy to compute. We study the theoretical properties of CDF and prove that the original problem and CDF have the same first-order and second-order stationary points, local minimizers, and Łojasiewicz exponents in a neighborhood of the feasible region. Remarkably, the convergence properties of our proposed constraint dissolving approaches can be directly inherited from the existing rich results in unconstrained optimization. Therefore, the proposed constraint dissolving approaches build up short cuts from unconstrained optimization to Riemannian optimization. Several illustrative examples further demonstrate the potenti...

刘歆，中国科学院数学与系统科学研究院“冯康首席研究员”，博士生导师，计算数学与科学工程计算研究所副所长。

刘歆2004年本科毕业于北京大学数学科学学院；并于2009年在中国科学院数学与系统科学研究院获得博士学位。主要研究方向包括流形优化、分布式优化及其在材料计算、大数据分析和机器学习等领域的应用。刘歆于2016年获得国家优秀青年科学基金；2016年获得中国运筹学会青年科技奖；2020年获得中国工业与应用数学学会应用数学青年科技奖；2021年获得国家杰出青年科学基金。现担任Mathematical Programming Computation、Journal of Computational Mathematics、Journal of Industrial and Management Optimization等国内外期刊编委；中国运筹学会常务理事，中国工业与应用数学会副秘书长。

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