This is a question re: Lost global definition after ifthenelse using package xifthen. I'll reference the Answer given in this question here since it's clear and clean.

MWE:

documentclass[parskip]{scrartcl}

usepackage[margin=15mm]{geometry}

usepackage{xifthen}



newcommand{test}[1]{%

ifthenelse{equal{#1}{}}{omitted}{given}%

}



begin{document}

par The optional argument was test.

par The optional argument was test[shubidu].

end{document}

Problem:

How to rewrite the command definition of test so that:

test{}

Output: omitted

test{shubidu}

Output: given

EDIT:

Thank you everyone for your tips and tricks. For some more information that may help clarify the purpose of this question:
I'm trying to define optional args using {} instead of because I'm in the process of making a TeX -> LyX transfer. LyX inserts an optional arg with if you click "Insert" on a drop-down menu and type the arg. Otherwise, LyX will insert your arg with {} if you do what I've done below. I would like to keep the formatting of what I've done below which is written with this: newcommand{BriefName}[1]{xdefBriefName{#1}} but make the argument inserted for BriefName optional. Thus, if the LyX user enters nothing in the BriefName line, the program still compiles, with an "empty" argument for the BriefName command.

Updated MWE:

This is more what I'm looking for. I created this thanks to this Q&A.

documentclass{article}

usepackage{xifthen}



newcommand{BriefName}[1]{ %

        xdefBriefName{#1}ifxBriefNameempty

          {}%

        else

          {#1}%

        fi

}%



begin{document}

par This should be empty:BriefName{}

par This should also be empty: BriefName

par This should say Argument: BriefName{Argument}

par This should also say Argument: BriefName

end{document}

You can do it with xparse; the trick is not redefining BriefName as you're trying to do, but another control sequence holding the current value (empty at the beginning).

documentclass{article}

usepackage{xparse}



ExplSyntaxOn

NewDocumentCommand{BriefName}{g}

 {

  IfNoValueF{#1}

   {

    tl_gset:Nn g_jalep_briefname_tl { #1 }

   }

  tl_use:N g_jalep_briefname_tl

 }

tl_new:N g_jalep_briefname_tl

ExplSyntaxOff



begin{document}



This should be empty:BriefName



This should also be empty: BriefName



This should say Argument: BriefName{Argument}



This should also say Argument: BriefName



end{document}

However, the standard LaTeX syntax uses for optional arguments, so it would be much better to stick with it.

documentclass{article}

usepackage{xparse}



ExplSyntaxOn

NewDocumentCommand{BriefName}{o}

 {

  IfNoValueF{#1}

   {

    tl_gset:Nn g_jalep_briefname_tl { #1 }

   }

  tl_use:N g_jalep_briefname_tl

 }

tl_new:N g_jalep_briefname_tl

ExplSyntaxOff



begin{document}



This should be empty:BriefName



This should also be empty: BriefName



This should say Argument: BriefName[Argument]



This should also say Argument: BriefName



end{document}

The version with also admits a solution with classical tools.

documentclass{article}



newcommand{BriefName}[1]{%

  ifrelaxdetokenize{#1}relax

  else

    gdefjalepbriefname{#1}%

  fi

  jalepbriefname

}

defjalepbriefname{}



begin{document}



This should be empty:BriefName



This should also be empty: BriefName



This should say Argument: BriefName[Argument]



This should also say Argument: BriefName



end{document}

To get what you ask you just need to delete in the declaration

documentclass[parskip]{scrartcl}

usepackage[margin=15mm]{geometry}

usepackage{xifthen}



newcommand{test}[1]{%

ifthenelse{equal{#1}{}}{omitted}{given}%

}



begin{document}



The optional argument was test{}.



The optional argument was test{shubidu}.



end{document}

However the original example appears to have been mis-using the optional argument syntax.

The intended syntax for the "not given" case is test not test

So you do not need to test for an empty argument, latex has already tested for [ being present:

documentclass[parskip]{scrartcl}

usepackage[margin=15mm]{geometry}

usepackage{xifthen}



newcommand{test}[1][default]{#1ldots}



begin{document}



The optional argument was test.



The optional argument was test[shubidu].



end{document}