I want to label a block of equations like that:

The "AB" should not inflict the central alignment of the formula. I saw it a lot, but do not succeed on my own. Do I need to build boxes?
I used the alignat environment for the formula.
I want to label a block of equations like that:

The "AB" should not inflict the central alignment of the formula. I saw it a lot, but do not succeed on my own. Do I need to build boxes?
I used the alignat environment for the formula.
amsmath's flalign environment stretches out the contents to be flush left and right. Here's how you can obtain your required output:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{flalign}
(\text{AB}) && z_{\text{LP}} = \min \sum_{p \in P} c_p\lambda_p & & \phantom{(\text{AB})} \\
&& \text{subject to\quad} \sum_{p \in P} \mathbf{a}_b\lambda_b &\geq \mathbf{b} \\
&& \sum_{p \in P} \lambda_p &= 1 \\
&& \lambda_p &\geq 0
\end{flalign}
\end{document}
The additional \phantom{..} on the right side is to obtain the required centered position of the other equation components (as a counterpart to the left (AB)).