报告题目：Optimization with Superquantile Constraints: A Fast Computational Approach
报 告 人：崔莹 助理教授（加利福尼亚大学伯克利分校）
报告时间：2024年7月4日（星期四）下午13:00-14:00
报告地点：数学科学学院115（大报告厅）
校内联系人：张立卫 教授 联系方式：84707354
报告摘要：We present an efficient and scalable second-order computational framework for solving large-scale optimization problems with superquantile constraints. Unlike empirical risk models, superquantile models have non-separable constraints that make typical first-order algorithms difficult to scale. We address the challenge by adopting a hybrid of the second-order semismooth Newton method and the augmented Lagrangian method, which takes advantage of the structured sparsity brought by the risk sensitive measures. The key to make the proposed computational framework scalable in terms of the number of training data is that the matrix-vector multiplication in solving the resulting Newton system can be computed in a reduced space due to the aforementioned sparsity. The computational cost per iteration for the Newton method is similar or even smaller than that of the first-order method. Our developed solver is expected to help improve the reliability and accuracy of statistical estimation and prediction, as well as control the risk of adverse events for safety-critical applications.
报告题目：A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex and Nonsmooth Recourse
报 告 人：崔莹 助理教授（加利福尼亚大学伯克利分校）
报告时间：2024年7月4日（星期四）下午14:00-15:00
报告地点：数学科学学院115（大报告厅）
校内联系人：张立卫 教授 联系方式：84707354
报告摘要：We study the decomposition methods for solving a class of nonconvex and nonsmooth two-stage stochastic programs, where both the objective and constraints of the second-stage problem depend on the first-stage variable nonlinearly. Such problems arise when the distributions of the random vectors in the second stage depend on the first-stage decisions. Due to the failure of the Clarke-regularity of the resulting nonconvex recourse function, classical decomposition approaches cannot be easily generalized to our problem. By exploring an implicitly convex-concave structure of the recourse function, we introduce a novel surrogate approach based on the so-called partial Moreau envelope. Convergence for both fixed scenarios and interior sampling strategy is established. Numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm.
报告题目：Variational Theory and Algorithms for a Class of Asymptotically Approachable Nonconvex Problems
报 告 人：崔莹 助理教授（加利福尼亚大学伯克利分校）
报告时间：2024年7月4日（星期四）下午15:00-16:00
报告地点：数学科学学院115（大报告厅）
校内联系人：张立卫 教授 联系方式：84707354
报告摘要：We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of this class is that the inner function can be merely lower semicontinuous instead of continuously differentiable. It covers a range of important yet challenging applications, including the composite value functions of nonlinear programs and the value-at-risk constraints. We propose an asymptotic decomposition of the composite function that guarantees epi-convergence to the original function, leading to necessary optimality conditions for the corresponding minimization problem. The proposed decomposition also enables us to design a numerical algorithm such that any accumulation point of the generated sequence, if exists, satisfies the newly introduced optimality conditions. These results expand on the study of so-called amenable functions introduced by Poliquin and Rockafellar in 1992, which are compositions of convex functions with smooth maps, and the prox-linear methods for their minimization.
报告人简介：Ying Cui is currently an assistant professor in the Department of Industrial Engineering and Operations Research at the University of California, Berkeley. Prior to that, she was an assistant professor at the University of Minnesota. She worked as postdoc research associate in the Daniel J. Epstein Department of Industrial and Systems Engineering at the University of Southern California. Cui completed her PhD in Mathematics at the National University of Singapore. Her research focuses on the mathematical foundation of data science with emphasis on optimization techniques for operations research, machine learning and statistical estimations. She is particularly interested in leveraging nonsmoothness to design efficient algorithms for large scale nonlinear optimization problems. She is the co-author of the recently published monograph “Modern Nonconvex Nondifferenable Optimization”.
