Dealing with widows in a multicol environment

I have problems with dealing with widows within a multicols environment, that is, I have not managed to instruct LaTeX to remove the them.

This PDF document shows an example of the problem. At the top of the second page, I get a widow from the last paragraph of the first page. I have tried a couple of approaches, without luck:

setting both \widowpenalty and \clubpenalty to high values
switching between \raggedcolumns and \flushcolumns
adjusting the collectmore and unbalance counters

I've also read through the documentation for multicol but have not found anything useful.

Is there anything else I could try?

(The complete LaTeX document for the above example)

Solution

{\obeyspaces\gdef\nomorebreak{\beginnomorebreak\let \nobreakspace}}
\def\beginnomorebreak{\begingroup
   \def\par{\endgraf\endgroup\par\penalty 9999 }\obeyspaces
   \brokenpenalty 10000 \widowpenalty 10000 \clubpenalty 10000 }
\def\nobreakspace{\vadjust{\nobreak} \removespaces}
\def\removespaces{\futurelet\next\checkspace}
\def\checkspace{\ifx\next\nobreakspace\expandafter\removesinglespace\fi}
\def\removesinglespace#1{\removespaces}

Insert \nomorebreak at any place of your paragraph. Page breaks will be prohibited after this macro until the end of the paragraph.