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Is there a way to replace "minimize" and "maximize" in optidef package with something that will display "exists"? I am wondering how to best typeset an existence problem in optidef, though maybe that's not the right package.

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You didn't specify what your intended input or output is. However, as a guess the following approach: you can use the customopti environment with the problem keyword as first (mandatory) argument.

MWE:

\documentclass{article}
\usepackage{optidef}
\begin{document}
\begin{customopti}
{exists}{w}{f(w)+ R(w+6x)}
{\label{eq:Example1}}{}
\addConstraint{g(w)}{=0}
\addConstraint{n(w)}{= 6}
\addConstraint{L(w)+r(x)}{=Kw+p}
\addConstraint{h(x)}{=0.}
\end{customopti}
\end{document}

Result:

enter image description here

Note that this requires the latest version from Github (https://github.com/jeslago/optidef/blob/master/optidef.sty), which is currently (June 2021) not yet on CTAN.

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    I'd be wary of using \DeclareDocumentEnvironment{exists}, because it silently overwrites the existing command \exists.
    – egreg
    Jun 23, 2021 at 17:32
  • @egreg good point, I changed the environment name.
    – Marijn
    Jun 23, 2021 at 17:34
  • @Marijn @egreg: Perhaps this could also be done using the customopti environment in optidef (see line 795 of github.com/jeslago/optidef/blob/master/optidef.sty) though it doesnt seem to be documented and when I tried it, it didn't seem to work for me
    – rrrrr
    Jun 23, 2021 at 17:41
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    @rrrrr that is much easier indeed :) my installed version of the package didn't have this environment yet. I edited the answer. The centering of subject to is also better in this version.
    – Marijn
    Jun 23, 2021 at 17:55

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