Minimax Theorems for Possibly Nonconvex Functions
Optimization and Control
2025-10-31 v1
Abstract
This paper establishes three minimax theorems for possibly nonconvex functions on Euclidean spaces or on infinite-dimensional Hilbert spaces. The theorems also guarantee the existence of saddle points. As a by-product, a complete solution to an interesting open problem related to continuously differentiable functions is obtained. The obtained results are analyzed via a concrete example.
Cite
@article{arxiv.2510.26710,
title = {Minimax Theorems for Possibly Nonconvex Functions},
author = {Nguyen Nang Thieu and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2510.26710},
year = {2025}
}