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Mathematics Colloquium

Baoyu Zhou
University of Michigan

Title: Next Generation Algorithms for Constrained Stochastic Optimization
Date: Wednesday, January 17, 2024
Place and Time: Love 101, 3:05-3:55 pm

Abstract. In this talk, we will discuss some recent works on the design, analysis, and implementation of efficient algorithms for solving stochastic optimization problems with constraints. Those optimization problems arise in a plethora of science and engineering applications including training deep neural networks, optimal power flow, optimal control, and online advertising. The first part of this talk focuses on an inexact regularized L-shaped algorithm for two-stage stochastic programming problems. In particular, we explain why such an algorithm performs so well in practice by providing the number of iterations, operations, and samples that the algorithm needs to find near-optimal solutions. In the second part of this talk, we will move our attention to the behavior of a class of sequential quadratic programming methods on general stochastic optimization problems with deterministic nonlinear constraints. In this case, projection-type methods are intractable since the feasible region of the problem could be difficult to detect. We demonstrate the efficiency and efficacy of our proposed method by presenting the algorithm’s theoretical convergence behavior as well as the empirical performance. In the end, I will conclude this talk with the discussion of potential future research directions.