Cómo configurar el ancho de la ecuación para que esté contenido dentro de una columna

Question

Estoy usando un diseño de dos columnas en mi archivo fuente de látex y tengo una serie de ecuaciones (de desigualdad) para mostrar, que quería mantener dentro de la columna de la izquierda. Sin embargo, con el entorno \begin{align*}, las ecuaciones desbordan la columna y ocupan algo de espacio adicional en la columna derecha. Puede consultar las imágenes que adjunto aquí para ver qué sucede. ¿Cómo puedo restringir las ecuaciones para que estén justo dentro de la primera columna?

Aquí está mi código fuente de látex. y aquí tienes un MWE que puedes probarte...

% \documentclass[conference]{IEEEtran}
\documentclass[10pt,conference,letterpaper]{IEEEtran}

\usepackage{amsmath}
\begin{document}

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
    \begin{align*}
        & \sum\nolimits_{e \in E^*} COST(g(e))\\
    &= \sum\nolimits_{e \in S_1} COST(g(e))
                                            + \sum\nolimits_{e \in S_2} COST(g(e))
                                            + \sum\nolimits_{e \in S_3} COST(g(e))\\
                        &\le 
                            2(1+\epsilon) COST(T^* \setminus T) 
                            +  COST(T^* \cap T)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                            &\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 2(1+\epsilon)COST(T^*)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4(1+\epsilon)OPT_n
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4+10\epsilon OPT_n
    \end{align*}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj




\end{document}

Answer 1

Esta es una posible solución. uso de resizeboxfrom graphicxpackage y parboxcombo como se muestra a continuación.

 \resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{ math envrionment}}

o

 {\tiny \begin{align*} ... \end{align*} environment} 

Código

\documentclass[10pt,conference,letterpaper]{IEEEtran}

\usepackage{amsmath,graphicx}
\begin{document}

as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
\resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{
    \begin{align*}
        & \sum\nolimits_{e \in E^*} COST(g(e))\\
    &= \sum\nolimits_{e \in S_1} COST(g(e))
                                            + \sum\nolimits_{e \in S_2} COST(g(e))
                                            + \sum\nolimits_{e \in S_3} COST(g(e))\\
                        &\le 
                            2(1+\epsilon) COST(T^* \setminus T) 
                            +  COST(T^* \cap T)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                            &\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 2(1+\epsilon)COST(T^*)
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4(1+\epsilon)OPT_n
                            + 4\epsilon OPT_n
                            + 2\epsilon OPT_n\\
                        &\le 4+10\epsilon OPT_n
    \end{align*}
}}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf  sfsdfkdf sdfks fksfksdfks fkf sdf sf  sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs 
\end{document}

Answer 2

Le sugiero que no tome ninguna medida que termine reduciendo el tamaño de fuente utilizado en la expresión matemática en relación con el utilizado para el texto circundante. En su lugar, es posible que desee seguir el siguiente enfoque:

• No utilices el \nolimitsmodificador después de cada \summacro. En su lugar, incluya las \sum{...}expresiones en \smashoperatordirectivas; esto reduce la cantidad de espacios en blanco antes y después de los signos de suma. (La \smashoperatormacro la proporciona el mathtoolspaquete, que es una extensión del amsmathpaquete (y lo carga).

• Inserte saltos de línea adicionales en las líneas 3 y 4.

• Opcional: renderice "COST" y "OPT" en tipo romano (vertical). Actualmente, TeX interpreta COST y OPT como grupos de variables de cuatro y tres letras, es decir, as C O S Ty as O P T, lo que lleva a un espaciado entre letras flojo y subóptimo. (Si desea representar los nombres de las variables en cursiva en lugar de en formato vertical, utilícelos \textiten lugar de \textupen las macros que definen \COSTy \OPT.)

\begin{align*}
& \smashoperator{\sum_{e \in E^*}} \COST(g(e))\\
&= \smashoperator{\sum_{e \in S_1}} \COST(g(e)) + 
   \smashoperator{\sum_{e \in S_2}} \COST(g(e)) + 
   \smashoperator{\sum_{e \in S_3}} \COST(g(e))\\
&\le 2(1+\epsilon) \COST(T^* \setminus T) + \COST(T^* \cap T)\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)(\COST(T^* \setminus T) + \COST(T^* \cap T))\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)\COST(T^*) + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4(1+\epsilon)\OPT_n + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4+10\eps

ilon \OPT_n \end{align*}