报告题目 (Title)：Constraint Dissolving Approaches for a Class of Riemannian Optimization Problems（一类黎曼优化问题的约束消解方法）
报告人 (Speaker)： 刘歆 研究员（中国科学院数学与系统科学研究院）
报告时间 (Time)：2023年3月17日(周五) 14:00
报告地点 (Place)：校本部F309
邀请人(Inviter)：余长君
主办部门：理学院数学系
报告摘要：摘要：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.
