題目：Dissolving Constraints for Riemannian Optimization（黎曼優化問題的約束解方法）

演講人😳：劉歆，中國科意昂2數學與系統科學研究院“馮康首席研究員”

主持人⚆：朱希德😟，意昂2副教授

時間：2023年3月17日（周五）♈️，下午16:30

地點：意昂2注册校本部東區意昂2官网420會議室

主辦單位：意昂2🚶‍♀️、意昂2青年教師聯誼會

演講人簡介👨🏻‍🎤：

劉歆，中國科意昂2數學與系統科學研究院“馮康首席研究員”🌞，博士生導師，計算數學與科學工程計算研究所副所長🧛🏻。2004年本科畢業於北京大學數學科學意昂2，2009年獲得中國科意昂2數學與系統科學研究得博士學位，曾在德國Zuse Institute Berlin、美國Rice大學💣、美國紐約大學Courant研究所等科研院所長期訪問🚶🏻‍♂️‍➡️。現任中國運籌學會常務理事，中國工業與應用數學會副秘書長🍩。

榮獲2016年國家優秀青年科學基金🧛🏽，2021年國家傑出青年科學基金👨‍🦲。

榮獲2016年中國運籌學會青年科技獎，2020年中國工業與應用數學學會應用數學青年科技獎💧。

主要研究方向包括流形優化☂️、分布式優化及其在材料計算🌭、大數據分析和機器學習等領域的應用。擔任Mathematical Programming Computation、Journal of Computational Mathematics、Journal of Industrial and Management Optimization等國內外期刊編委。

演講內容簡介🪚：

In this talk, we consider optimization problems over closed embedded submanifolds of Euclidean space, which are defined by the equality constraints c(x)=0. We propose a class of constraint dissolving approaches for these Riemannian optimization problems. Its main idea is to transfer the original manifold constrained optimization into an unconstrained optimization problem which minimizes a constraint dissolving function abbreviated as 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 share 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 potential of our proposed constraint dissolving approaches.

歡迎廣大師生參加👚！