Trouble with align environment

Question

Edited

I am having trouble using the alignenvironment, which I've read is a better alternative to eqnarrayto align equations.

Hereafter I display the PDF output of my Latex code:

I would like the max to be aligned with the \forall:

The code that I've written is the following:

\begin{align*}
\max_{\lambda,\lambda_0} M
\\
\forall i \in \{1,...,n\}, &\; \frac{y_i f(\mathbf{x}_i)}{\|\vec{\lambda}\|} \geq M 
\\
&\; \Leftrightarrow y_i \left(\frac{\vec{\lambda}^{\:T} \mathbf{x}_i+\lambda_0}{\|\vec{\lambda}\|}\right) \geq M 
\end{align*}

Would someone kindly point out what am I getting wrong?

Answer 1

The following solution nests an aligned environment inside an align* environment.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
&\max_{\lambda,\lambda_0} M\\
&\,\forall i \in \{1,\dots,n\}, 
  \begin{aligned}[t]
    &\frac{y_i f(\mathbf{x}_i)} {\|\vec{\lambda}\|} \geq M \\
    &\Leftrightarrow y_i \biggl(\frac{\vec{\lambda}^{\:T} 
        \mathbf{x}_i+\lambda_0}{\|\vec{\lambda}\|}\biggr) \geq M
  \end{aligned}
\end{align*}
\end{document}

Answer 2

Maybe this is the desired output:

documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{2}
&\! % or \max would be a bit to the right
\max_{\lambda,\lambda_0} M
\\
&\forall i \in \{1,\dots,n\},
&&\frac{y_i f(\mathbf{x}_i)}{\|\vec{\lambda}\|} \geq M
\\
&& \Leftrightarrow {} &
  y_i \left(\frac{\vec{\lambda}^{\,T}
  \mathbf{x}_i+\lambda_0}{\|\vec{\lambda}\|}\right) \geq M
\end{alignat*}

\end{document}