# Minimax theorems in a fully non-convex setting

## TL;DR

This paper proves two minimax theorems for functions without the usual quasi-concavity assumption, broadening the theoretical framework for non-convex optimization problems.

## Contribution

It introduces minimax theorems applicable to fully non-convex functions, expanding the scope of minimax theory beyond traditional convexity constraints.

## Key findings

- Established two minimax theorems without quasi-concavity assumptions
- Extended minimax theory to fully non-convex functions
- Presented applications of the new theorems

## Abstract

In this paper, we establish two minimax theorems for functions $f:X\times I\to {\bf R}$, where $I$ is a real interval, without assuming that $f(x,\cdot)$ is quasi-concave. Also, some related applications are presented.