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I am a newbie to LaTeX and would like to write this optimization problem using LaTeX code:

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I would very appreciate it if someone could help me.

enter image description here

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    Welcome to TeX.SX! You can have a look at our starter guide to familiarize yourself further with our format.
    – CarLaTeX
    Feb 21 '18 at 3:58
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Just to give you a starting point. This is how I may type this in TeX.

\documentclass{article} 
\usepackage{amsmath}
\DeclareMathOperator{\var}{var}
\begin{document}
\[ \underset{w1,w2\cdots w_{20}}{\text{min}/\text{max}}\,w^TCw
\quad\text{subject to}\begin{cases}
(1) & w_1+w_2+\cdots +w_{20}=100\%\\
(2) & 0\%\le w_i\le100\%\quad\forall i=1,2,\dots 20
\end{cases}
\]

\[ \max_{w1,w2\cdots w_{20}}E[w_1R_1+w_2R2+\cdots+w_{20}R{20}]
\quad\text{subject to}\begin{cases}
(1) & \sqrt{\var[w_1R_1+\cdots+w_{20}R_{20}]}\le \sigma_\mathrm{max}\\
(2) & w_1+w_2+\cdots +w_{20}=100\%\\
(3) & \ell_i\le w_i\le u_i\quad\forall i=1,2,\dots 20
\end{cases}
\]
\end{document}
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  • Thank you so much for your help. I was just wondering if you could one more time writing LaTeX.... this is so hard lol.
    – Jun Jang
    Feb 21 '18 at 15:16
  • @JunJang Sorry, I don't understand " I was just wondering if you could one more time writing ". What precisely am I supposed to do?
    – user121799
    Feb 21 '18 at 15:18
  • Oh sorry. I meant "I was just wondering if you could help me one more time writing LaTeX". sorry for the confusion!
    – Jun Jang
    Feb 21 '18 at 15:19
  • @JunJang Sure. But what?
    – user121799
    Feb 21 '18 at 15:19
  • I just added a new capture in the post. I would like to write the optimization problem in LaTex code too.
    – Jun Jang
    Feb 21 '18 at 15:21

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