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arXiv · 2510.26710

Minimax Theorems for Possibly Nonconvex Functions

Nguyen Nang Thieu·Nguyen Dong Yen
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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.

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Nguyen Nang Thieu, Nguyen Dong Yen. 2025-10-30. Minimax Theorems for Possibly Nonconvex Functions. https://arxiv.org/abs/2510.26710

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