English

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.

Keywords

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}
}
R2 v1 2026-07-01T07:14:13.542Z