学术报告

题      目：Nonsmooth Nonconvex-Nonconcave Min-Max Optimization Problems

报  告  人：Xiaojun Chen  教授  (邀请人：黎稳 )

                                    The Hong Kong Polytechnic University

时      间：4月2日  10：30-11：30

地     点：数科院阶梯二楼报告厅

报告人简介:

        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 90 papers in top journals in applied mathematics. She is an Associate Editor of  SIAM J. Optimization, SIAM J. Numerical Analysis, SIAM J. Control and Optimization, and the Area Editor of Journal on Optimization Theory and Applications. She is a fellow of  Society for Industrial and Applied Mathematics and a fellow of American Mathematical Society. She is a Keynote speaker of the 25th International Symposium on Mathematical Programming in Canada 2024.

摘      要：

        This talk considers nonsmooth nonconvex-nonconcave min-max optimization problems with convex feasible sets.  We discuss the existence of local saddle points, global minmax points and local minimax points, and study the optimality conditions for local minimax points. We show the existence of local saddle points and global minimax points of convex-concave saddle point problems with cardinality penalties and its continuous relaxation problems.  Moreover, we give an explicit formula for the value function of the inner maximization problem of a class of robust nonlinear least square problems and complexity bound for finding an approximate first order stationary point.  A smoothing quasi-Newton subspace trust region algorithm is presented for training generative adversarial networks as nonsmooth nonconvex-nonconcave min-max optimization problems.  Examples of retinal vessel segmentation in fundoscopic images are used to illustrate the efficiency of the algorithm.

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