Typesetting an optimization problem in one line enumerated with numbers

Question

Can someone help me to typeset the following optimization problem:

Answer 1

The following should produce your equation:

\documentclass[]{article}

\usepackage[]{amsmath}

\begin{document}
\begin{equation}
  \min\lVert z\rVert_{1}\quad\text{subject to}\quad
  \lVert Az - y\rVert_{2} \leq \eta\quad\text{and}\quad
  z\in [0,1]^{N}.
  \tag{$\mathrm{P}^{\eta}_{\mathrm{bin}}$}
\end{equation}
\end{document}

Answer 2

I add only a complement using optidef package useful for optimization of the problems.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{optidef}
\begin{document}
\begin{mini*} 
{}{\lVert z\rVert_{1}}{}{}\tag{$\mathrm{P}^{\eta}_{\text{bin}}$}
\addConstraint {\lVert Az-y \rVert_{2}}{\leq \eta,}{\quad \text{ and } z\in [0,1]^{N}.} 
\end{mini*}
\end{document}