Hi I want to find the relationship between two convex programs
**************************P1: \begin{equation} Z_1 = \min_x f(x) \end{equation} S.T. \begin{equation} Ax = b\\ \sum_{ij}x_{ij} = 1\\ 0 \le x_{i,j} \le 1 \end{equation}
**************************P2: \begin{equation} Z_2 = \min_x f(x) \end{equation} S.T. \begin{equation} Ax = b\\ \sum_{i}x_{ij} = 1, \forall j\\ 0 \le x_{i,j} \le 1 \end{equation}
How do I proceed to find a relationship b below-
$Z_1 \overset{?}{b} Z_2$
i.e. whether $b$ is $"\le", "\ge"$ or $=$?
In the above program, $f$ is a convex function.