Deterministic and Stochastic Accelerated Gradient Method for Convex Semi-Infinite Optimization
Year: 2023
Type: preprint
Abstract: This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint parameters, a momentum gradient ascend step to update the dual variables, and a gradient descend step to update the primal variables. Our approach also extends to scenarios where gradients and function values are accessible solely through stochastic oracles. This method extends the recent primal-dual methods, for example, Hamedani and Aybat (2021); Boob et al. (2022), for optimization with a finite number of constraints. We show the iteration complexity of the proposed method for finding an $ε$-optimal solution under different convexity and concavity assumptions on the functions.
Source: arXiv (Cornell University)
Authors: Yao, Yao, Lin, Qihang, Yang, Tianbao
Institutions: University of Iowa, Texas A&M University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4387797182