Aligning a optimization equation

Question

I was trying to write a optimization formula which has two part as objective and 2 constraints. But, the objective function is a little bigger and i want to see it in multiline not in single line. But it's not working the way i want it to work. Can someone provide me some good suggestion about how to make it in multiline while the objective function is one equation and constraints are assigned as separate equation. The LaTeX code is like this:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{align}
\label{green}
\text{minimize } & \quad {\sum\nolimits_{\tau=t}^{t+T-1}}s(\tau)[V(\t)-x(\tau)-y(\tau)-Y(\tau)] +{\sum\nolimits_{\tau=t}^{t+T-1}}[(X(\tau)+Y(\tau))(b(\tau)-v(\tau))] \\
\text{subject to } & \quad \quad {something1}\\
& \quad \quad {something 2} 
\end{align}

\end{document}

Answer 1

You can use split inside align:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align}
\begin{split}
\text{minimize}\qquad &
  \sum_{\tau=t}^{t+T-1} s(\tau)[V\beta(\tau)-Q(\tau)-X(\tau)-Y(\tau)] \\
  &\qquad  +\sum_{\tau=t}^{t+T-1} [(X(\tau)+Y(\tau))(\gamma b(\tau)-\gamma v(\tau))]
  \end{split}
\label{green} 
\\[2ex]
\text{subject to}\qquad & 0\leq s(\tau)\leq s_{\textup{max}}, \quad \forall \tau   
\label{green-constraint-1} 
\\
& \sum_{\tau=t}^{t+T-1} \gamma \beta(\tau)\leq N_{\textup{max}}
\label{green-constraint-2}
\end{align}

Check: \eqref{green} with \eqref{green-constraint-1} and \eqref{green-constraint-2}.

\end{document}

Answer 2

I suggest using the \MoveEqLeft command from mathtools and having only one number for the constraints. If your want independent numbring of constraints, I have a solution with alignat:

    \documentclass[a4paper, 11pt]{book}
\usepackage[utf8]{inputenc}
\usepackage{fourier, heuristica}
\usepackage[showframe, nomarginpar]{geometry}

\usepackage{mathtools, cases}

\begin{document}

\begin{align}
\label{green}
\MoveEqLeft\text{Minimize: }\notag\\
& \quad {∑_{\tau=t}^{t+T-1}}s(τ)\bigl[Vβ(τ)-Q(τ)-X(τ)-Y(τ)\bigr] +{∑_{\tau=t}^{t+T-1}}\bigl[(X(τ)+Y(τ))(γ b(τ)-γ v(τ))\bigr] \\
 \MoveEqLeft\text{subject to}
\qquad \!\begin{cases}
\hspace*{0.5em} 0 \leq s(τ)\leq s_{\max}, \quad ∀ τ \\
\hspace*{0.5em}\displaystyle∑_{\mathclap{\tau=t}}^{\mathclap{t+T-1}} γ β(τ)\leq N_{\max}
\end{cases}
\end{align}


\begin{alignat}{2}
\label{green}
\MoveEqLeft[2]\text{Minimize: }\notag\\
& ∑_{\tau=t}^{t+T-1}s(τ) & &\bigl[Vβ(τ)-Q(τ)-X(τ)-Y(τ)\bigr] +{∑_{\tau=t}^{t+T-1}}\bigl[(X(τ)+Y(τ))(γ b(τ)-γ v(τ))\bigr] \\[1ex]
 \MoveEqLeft \text{subject to}
 & & 0 \leq s(τ)\leq s_{\max}, \quad ∀ τ \\
& & & \displaystyle∑_{\mathclap{\tau=t}}^{\mathclap{t+T-1}} γ β(τ)\leq N_{\max}
\end{alignat}

\end{document} 

Answer 3

Do you want something like this?

% arara: pdflatex

\documentclass{article}
\usepackage{mathtools}
\usepackage{blindtext}

\begin{document}
\blindtext
\begin{align}
    \shortintertext{Minimize}   
    \MoveEqLeft[3]\sum\nolimits_{\tau=t}^{t+T-1}s(\tau)[V\beta(\tau)-Q(\tau)-X(\tau)-Y(\tau)] \nonumber \\
    +{}&\sum\nolimits_{\tau=t}^{t+T-1}[(X(\tau)+Y(\tau))(\gamma b(\tau)-\gamma v(\tau))]\label{green}\\
    \shortintertext{subject to} 
    &0\leq s(\tau)\leq s_\text{max}, \quad \forall \tau \\  
    &\sum\nolimits_{\tau=t}^{t+T-1} \gamma \beta(\tau)\leq N_\text{max}
\end{align} 
\blindtext
\end{document}