How do I write a cursive U in math mode for uncertainty sets?

If you’re using LuaLaTeX or XeLaTeX, you want to load unicode-math and a math font of your choice. The default Latin Modern Math mathcal is pretty close in that specimen sheet, but you could use, for example, the mathcal from STIX Two Math with:

setmathfont{Latin Modern Math}
setmathfont{STIX Two Math}[
   range={cal,bfcal},
   Scale=MatchUppercase ]

There’s a more complete list of OpenType math fonts that you can try on this site.

With PDFTeX, the best way to change supplementary math alphabets is mathalpha. The manual has a comprehensive set of specimens, but you might try

usepackage[cal=esstix]{mathalpha}

with a calscaled= parameter if you need to adjust the size.

If you are using OpTeX, then load appropriate Unicode font family and use {cal U} or directly ?. For example:

fontfam[lmfonts]

... subject to $f_i(x,u)le 0$ for $uin{cal U}$, $i=1,dots,m$.

or

... subject to $f_i(x,u) ≤ 0$ for $u ∈ ?$, $i = 1,dots, m$.

bye

Off-topic...I think..But if you want to create your image in LaTeX code you can use optidef package that it is specific.

documentclass[12pt]{article}
usepackage{amsmath,amssymb}
usepackage{optidef}

begin{document}
begin{mini}<b>
{}{f_0(x)}{}{}
addConstraint {f_i(x,u)}{le 0text{ for all } uinmathcal{U},,}{i=1,ldots,m}
end{mini}
end{document}