題目：Constraint dissolving: a powerful tool for Riemannian optimization

  内容簡介：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 potential of the proposed approaches.

  報告人：劉歆

  報告人簡介：中國科學院數學與系統科學研究院研究員，博士生導師，計算數學與科學工程計算研究所副所長。2004年本科畢業于北京大學數學科學學院；并于2009年在中國科學院數學與系統科學研究院獲得博士學位。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。分别于2016年，2021年和2023年獲得國家自然科學基金委優秀青年科學基金項目、傑出青年科學基金項目和科技部重點專項的資助。2024年獲得中國工業與應用數學學會蕭樹鐵應用數學獎。現擔任MPC, JCM, APJOR等國内外期刊編委，《中國科學·數學》（中英文）青年編委，《計算數學》副主編；中國科學院青年創新促進會理事長；中國運籌學會常務理事；中國工業與應用數學會副秘書長，中國數學會計算數學分會常務理事。

  時間：2025年3月14日（周五） 10：00

  地點：石牌校區南海樓338會議室