Help formatting my optimization problem

i'm doing some slides with the beamer class. I got an optimization problem that i couldn't make it fit in a single slide, as you can see here (the last constraint is being cut out): This is my code:

\tiny
\begin{equation}
\label{modelo_mat}
\begin{aligned}
& \text{minimize}
&& \sum_{i=1}^{N} (w_1DTT3_i+w_2DTTI_i+w_3a_i)\\
& \text{sujeito a:}
&& y_{fi}^h = \frac{1}{\dfrac{X_{Cfi}}{f_Q h_{si}}+j\left(\dfrac{hX_{Cfi}}{h_{si}^2}-\dfrac{X_{Cfi}}{h}\right)} \quad i = 1,2, ..., N \quad h = 3,5,7,...  \\
&&& \textbf Y^h \textbf V^h = \textbf I^h \quad h = 3,5,7,...,h_{max}\\
&&& DTT3_i = \frac{\sqrt{\sum_h V_i^{h^2}}}{U_i}\times 100\% , \quad i = 1,2,...,N \quad h = 3,9,15, ... \\
&&& DTTI_i = \frac{\sqrt{\sum_h V_i^{h^2}}}{U_i}\times 100\% , \quad i = 1,2,...,N \quad h = 5,7,11, ... \\
&&& DTT3_i \le \overline{DTT3_i} \quad i = 1,2,...,N \\
&&& DTTI_i \le \overline{DTTI_i} \quad i = 1,2,...,N \\
&&& \ubar{h}_{si} \le h_{si} \le \bar{h}_{si} \quad i = 1,2,...,N \\
&&& a_i \in \{0,1\} \quad i = 1,2,...,N \\
\end{aligned}
\end{equation}
\normalsize

How can i change it to make it fit in a single slide?

• Please make your code fragment compilable. – Zarko Jul 17 at 22:04
• At the end of the line you can use \\[-3pt] to reduce the interline space. – vi pa Jul 19 at 11:13

see if the following modification of your code fragment fit on your slide:

\tiny
\begin{equation}
\label{modelo_mat}
\begin{aligned}
& \text{minimize}
&& \sum_{i=1}^{N} (w_1DTT3_i+w_2DTTI_i+w_3a_i)\\
& \text{sujeito a:}
&& y_{fi}^h = \left[\dfrac{X_{Cfi}}{f_Q h_{si}}+j\left(\dfrac{hX_{Cfi}}{h_{si}^2}-\dfrac{X_{Cfi}}{h}\right)\right]^{-1}, \quad i = 1,2, ..., N \quad h = 3,5,7,...  \\
&&& \textbf Y^h \textbf V^h = \textbf I^h \quad h = 3,5,7,...,h_{max}\\
&&& DTT3_i = \frac{1}{U_i}\sqrt{\sum\nolimits_h V_i^{h^2}}\times 100\% , \quad i = 1,2,...,N \quad h = 3,9,15, ... \\
&&& DTTI_i = \frac{1}{U_i}\sqrt{\sum\nolimits_h V_i^{h^2}}{U_i}\times 100\% , \quad i = 1,2,...,N \quad h = 5,7,11, ... \\
&&& DTT3_i \le \overline{DTT3_i} \quad i = 1,2,...,N \\
&&& DTTI_i \le \overline{DTTI_i} \quad i = 1,2,...,N \\
&&& \bar{h}_{si} \le h_{si} \le \bar{h}_{si} \quad i = 1,2,...,N
a_i \in \{0,1\} \quad i = 1,2,...,N \\
\end{aligned}
\end{equation}

it gives: I propose this layout:

\documentclass{beamer}
\usepackage{mathtools, nccmath}
\usepackage{accents}
\newcommand{\ubar}{\underaccent{\bar}{#1}}

\setbeamersize{text margin left = 5mm,text margin right = 5mm}

\begin{document}

\section{Methods and Materials}

\begin{frame}
\begin{equation}
\label{modelo_mat}
\begin{alignedat}{3}
& \text{minimize}
&& \sum_{i=1}^{N} (w_1DTT3_i+w_2DTTI_i+w_3a_i)\\
& \text{sujeito a: } & & \forall i = 1,2, ..., N, \\
&& & y_{fi}^h = \frac{1}{\mfrac{X_{Cfi}}{f_Q h_{si}}+j\left(\mfrac{hX_{Cfi}}{h_{si}^2}-\mfrac{X_{Cfi}}{h}\right)}, & \hspace*{-1.7em}& h = 3,5,7,... \\
&&& \textbf Y^h \textbf V^h = \textbf I^h &\hspace*{-1.7em} & h = 3,5,7,...,h_{\rlap{\small max}}\\
&&& DTT3_i = \medmath{\frac{\sqrt{\sum_h V_i^{h^2}}}{U_i}\times 100\% }, & \hspace*{-1.7em} & h = 3,9,15,... \\
&&& DTTI_i =\medmath{ \frac{\sqrt{\sum_h V_i^{h^2}}}{U_i}\times 100\% , }& \hspace*{-1.7em} & h =5,7, 11,... \\
&&& DTT3_i \le \overline{DTT3_i} \\
&&& DTTI_i \le \overline{DTTI_i} \\
&&& \ubar{h}_{si} \le h_{si} \le \bar{h}_{si}\\
&&& a_i \in \{0,1\}
\end{alignedat}
\end{equation}
\end{frame}

\end{document} 