I have taken an optimization course but It seems that I don't have its basics so any reference would be appreciated,
In the publication , it is stated
any limit point satisfies the Nash equilibrium conditions.
After reading I knew that Nash equilibrium is related to game theory where one of 2 participants can't gain by change of strategy as long as as the other participant is on the same strategy.
I also found that limit point is the stationary point and in other documents that it is the result of the limits operation, where a point doesn't exist in a set but tends to get close to it.
My problem is that I can't relate both of them.
Definition of Nash point in the paper in page 6 for objective function,
\begin{equation*} \begin{aligned} & \underset{x \in \mathcal{X} }{\text{minimize}} & & F(x_1, ...,x_s) = f(x_1,...,x_s) + \sum_{i=1}^s (r_i(x_i)) \\ & \text{subject to} & & F(x_i) \geqslant 0 , \quad where \quad i = 1, ...,s \end{aligned} \end{equation*}
is
\begin{equation*} F(x^*_1,x_{i-1}^*,x_i^*,x_{i+1}^*,...,x_s^*) \leqslant F(x^*_1,x_{i-1}^*,x_i,x_{i+1}^*,...,x_s^*), \forall x_i \in \mathcal{X_i^*} \\ \mathcal{X_i^*} = \mathcal{X_i}(x_1^*,...,x_{i-1}^*,x_{i+1}^*,...,x_s^*) \end{equation*}
where $x_i^*$ is a Nash point.