[IMS Seminar] On the global convergence of coordinate gradient descent for non-convex optimization

ON2022-09-20TAG: ShanghaiTech UniversityCATEGORY: Lecture

Time:Friday, September 23th, 2022, 15:30-16:45

Location:R408, IMS(创艺学院南楼408教室)


Speaker:  Yingzhou Li, Fudan University

Abstract: Coordinate descent descent methods are considered for eigenvalue problems based on a reformulation of the leading eigenvalue problem as a nonconvex optimization problem. The convergence of several deterministic coordinate methods is analyzed and compared. We also analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinate descent methods.