Latex, left indent numcases

Question

I have this simple equation (representation a dynamic programming recursion):

 \begin{numcases}
{Opt\left(P, i, \ell \right)=min }
\nonumber (1)\hspace{0.5 mm} Opt(P,i+1,\ell) + M(\ell,g)\label{eq:1}\hspace*{-10em} & \\
\nonumber (2)\hspace{0.5 mm} \min_{g \in L(v_{i+1})}\{Opt(P,i+1,g) + M(\ell,g)\}\label{eq:2}\hspace*{-5em} & \\
\end{numcases}

I have three questions:

1) How do I remove the equation number automatically added, I tried \nonumber but it didn't work.

2) More importantly, how do I control the left indent. Latex automatically centers the equations, but I am using a double column paper template and I would like the equation to be aligned to the left in this case, or at the very least control the left indent.

3) Is it possible in Latex to take any piece of latex code and rescale its output? For example I would like to place this exact equation but make it 90% of its original size.

Answer 1

Your answer would have been self-evident have you provided an MWE. You must have something like the code below.

\documentclass[twocolumn,fleqn]{article} % The fleqn option left aligns equations

\usepackage[outer=0.2in,inner=0.1in]{geometry}
\usepackage{cases}
\setlength{\mathindent}{0cm}

\begin{document}

\begin{numcases}
{Opt\left(P, i, \ell \right)=min }
 (1)\hspace{0.5 mm} Opt(P,i+1,\ell) + M(\ell,g)\label{eq:1}\hspace*{-10em} & \nonumber\\ % Put the command \nonumber before \\ and do not put \\ after the last line in order not to create a new equation line.
 (2)\hspace{0.5 mm} \min_{g \in L(v_{i+1})}\{Opt(P,i+1,g) + M(\ell,g)\}\label{eq:2}\hspace*{-5em} & \nonumber
\end{numcases}


\end{document}