optimization formulas latex

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{aligned}
\min_{w,b,\xi} \quad & \frac{1}{2}w^{t}w+C\sum_{i=1}^{N}{\xi_{i}}\\
\textrm{s.t.} \quad & y_{i}(w\phi(x_{i}+b))+\xi_{i}-1\\
  &\xi\geq0    \\
\end{aligned}
\end{equation}
\end{document}