报告题目:Complexity of Projected Gradient Methods for Strongly Convex Optimization with H"older Continuous Gradient Terms

报  告 人:陈小君讲座教授（ 香港理工大学）

报告时间: 3月9日(周一) 上午10：00-11：00

报告地点:广东工业大学龙洞校区行政楼610室

Abstract：This talk presents new complexity bounds of projected gradient descent methods for a class of strongly convex constrained optimization problems where the objective function is expressed as a summation of finite component functions, each possessing a gradient that is H"older continuous with an exponent alpha in (0, 1]. Under this formulation, the gradient of the objective function may fail to be globally H"older continuous, thereby existing complexity results inapplicable to this class of problems. We first give the complexity bound of the projected gradient descent method with an appropriate fixed stepsize for finding an epsilon approximate minimizer, which extends the well-known complexity result. Next we show that the complexity bound can be improved if the stepsize is updated by the universal scheme. We illustrate our complexity results by numerical examples arising from elliptic equations with a non-Lipschitz term. This is a joint work with Tim Kelley and Lei Wang.

个人简介： Xiaojun Chen is a Chair Professor of Department of Applied Mathematics, Hong Kong Polytechnic University.  She is the Co-Director of CAS AMSS-PolyU Joint Laboratory of Applied Mathematics.   Her research interests focus on mathematical optimization theory and algorithms for nonsmooth nonconvex optimization problems and stochastic variational inequalities with applications in data sciences. She is the PI of several large grants from Hong Kong Research Grant Council and Croucher Foundation.  She published over 100 papers in top journals in applied mathematics.  She is an Area Editor of Journal of Optimization Theory and Applications. She served/serves SIAM Journal on Numerical Analysis, SIAM Journal on Optimization and SIAM Journal on Control and Optimization as an Associate Editor. She is a fellow of Society for Industrial and Applied Mathematics (SIAM) and a fellow of American Mathematical Society (AMS). She is a Keynote speaker of the 25^th International Symposium on Mathematical Programming in Canada 2024 and  the 16^th Viennese Conference on Optimal Control and Dynamic Games in Austria 2025, and an invited 45-minute speaker in the International Congress of Mathematics (ICM) in Philadelphia 2026.