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5 votes

Can we add a certain binary row to a matrix which preserves total unimodularity?

Your conjecture is wrong as the following counterexample demonstrates. Consider $$ A = \begin{pmatrix} 1 & 0 & -1 \\ 1 & 1 & 0 \end{pmatrix} $$ and $$ b^\top = \begin{pmatrix} -1 & ...
joni's user avatar
  • 1,562
1 vote

Small number of constraints, but very large coefficients

If you can make it work with $10^{-6}$ or $10^{-8}$ relative precision, just use an off-the-shelf solver with more precision-oriented options. You will need to rescale your problem so that the ...
Ggouvine's user avatar
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1 vote

Small number of constraints, but very large coefficients

Classical MILP solvers work with floating-point numbers. Therefore, if you need more accuracy than what a double might store, they won't fit. Otherwise, what is important first for numerical stability ...
fontanf's user avatar
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0 votes

How to linearize a product of an integer and a binary variable

Some comments already hinted at questions that give you the answer. In your specific example, this translates to the following: \begin{align} 0 \leq number_t \leq (number_{t−1}+new_t) \newline ...
PeterD's user avatar
  • 1,501

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