Continuous Optimization Team (Talk by Yuntian Jiang, Shanghai University of Finance and Economics)

The Continuous Optimization Team hosts an online research talk by Yuntian Jiang of Shanghai University of Finance and Economics, titled "A New Trust Region Method with Advanced Complexity Analyses". The trust-region method is prized for its numerical robustness, but its theoretical guarantees in convex optimization and global acceleration remain underexplored. This talk addresses those gaps through two connected works. The first part introduces a universal trust-region framework that combines quadratic regularization with ball constraints. A novel descent property unifies the analysis for convex and nonconvex optimization, yielding strong iteration complexity bounds for convex problems and for finding approximate second-order stationary points in nonconvex settings. The second part tackles the trade-off between global efficiency and fast local convergence in second-order methods. The speaker presents the first accelerated trust-region-type methods, which exploit inherent primal-dual information to achieve improved global oracle complexity while strictly maintaining quadratic local convergence, and establishes a theoretical phase transition: pushing global efficiency to its limit inherently breaks quadratic local convergence.