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If you can't find (or can't afford) a solver that will handle a problem with that many nonzero matrix coefficients, and if your problem has a structure that fits one of the following methods, you might try either Dantzig-Wolfe or Benders decomposition.


I think it is not easy (at least for me) to formulate the deviation part, so let's omit it... Let decision variable $b_i = 1$ if $x_i$ is chosen, otherwise $b_i = 0$. The mean value is defined by $$ \sum b_i \bar{X} = \sum b_ix_i. $$ To vanish the bilinear term, introduce new variables $y_i$, to ensure $$ y_i = b_i\bar{X}, $$ introduce constraints $$ -Mb_i \...

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