documentclass{beamer}
usepackage{amsmath}
DeclareMathOperator*{minimize}{minimize}
begin{document}
begin{frame}[t]
frametitle{A slide}
[minimize_{{alpha}} |boldsymbol{mathrm{i}}-boldsymbol{Phimathcal{D}alpha}|_2
+lambda |boldsymbol{alpha}|_1]
or
$displaystyleminimize_{{alpha}} |boldsymbol{mathrm{i}}-boldsymbol{Phimathcal{D}alpha}|_2
+lambda |boldsymbol{alpha}|_1$
end{frame}
end{document}