Math & Science ⇒ Numbering Aligned Equations, and writing under Min

[amegahed3]

Hi All,

I'm a beginner in Latex, and I have the following 3 questions:

1. The following code writes my equations in the exact same way I want them to appear. The only thing left is that I need to have each equation numbered by a separate number instead of just one number for the three equations, as the case now. What shall I do? the code is:

Code: Select all

\begin{equation}
\begin{aligned}
\mbox{min}  ~~ ~~ &\sum \limits_{s \in S} C_s F_s  +  \sum \limits_{(i,j) \in A} \sum \limits_{t \in T} K_{ijt} (\omega)\\
\mbox{s.t.} ~~ ~~ &\sum \limits_{s \in S} a_{ijts} F_{s} + K_{ijt} (\omega) \geq l_{ijt}(\omega) ~~ \forall (i,j) \in A,~~ \forall t \in T\\
& F_{s}, K_{ijt} (\omega) \in \mathbb{Z}_{+}\\
\end{aligned}
\end{equation}

2. In the previous code as well, how can I align the equations to the left, instead of centered? So, I want their relative alignment the same as they appear now, but I want them all to begin from the left, not from the center. How can that be done?

3. I wanna write x \in X under Min. How can that be done, given that this is inside the equation? So, my code is:

Code: Select all

\begin{equation}
\begin{aligned}
Min_{x \in X} ~~     \{ g(x):=c^{T}x+E [ Q(x, \xi(\omega))]\}\\
Q(x,\xi):=inf_{y \in Y} \{q^{T}y:Wy \geq h-Tx\}\\
\end{aligned}
\end{equation}

Where that code writes x \in X as a subscript of Min, but I want it under Min. I tried \limits, but seems like it just works with math stuff (like \sum). Any ideas?

Any help will be really appreciated!

Thanks in advance!

Aly

[Stefan Kottwitz]

Hi Aly,

1. Use the align environment instead of equation and aligned:

   Code: Select all

       \begin{align}
       \mbox{min}  ~~ ~~ &\sum \limits_{s \in S} C_s F_s  +  \sum \limits_{(i,j) \in A} \sum \limits_{t \in T} K_{ijt} (\omega)\\
       \mbox{s.t.} ~~ ~~ &\sum \limits_{s \in S} a_{ijts} F_{s} + K_{ijt} (\omega) \geq l_{ijt}(\omega) ~~ \forall (i,j) \in A,~~ \forall t \in T\\
       & F_{s}, K_{ijt} (\omega) \in \mathbb{Z}_{+}
       \end{align}
   

2. You could use the flalign environment:

   Code: Select all

       \begin{flalign}
       \mbox{min}  ~~ ~~ &\sum \limits_{s \in S} C_s F_s  +  \sum \limits_{(i,j) \in A} \sum \limits_{t \in T} K_{ijt} (\omega)&\\
       \mbox{s.t.} ~~ ~~ &\sum \limits_{s \in S} a_{ijts} F_{s} + K_{ijt} (\omega) \geq l_{ijt}(\omega) ~~ \forall (i,j) \in A,~~ \forall t \in T&\\
       & F_{s}, K_{ijt} (\omega) \in \mathbb{Z}_{+}&
       \end{flalign}
   

   or the fleqn option for the whole document.
3. Declare Min as operator:

   Code: Select all

   \DeclareMathOperator*{\Min}{Min}

Stefan

[amegahed3]

Thanks a lot, Stefan. All your tricks worked perfectly. Thanks.

Aly