Constraint Reduction for Linear Programs with Many Inequality Constraints

Consider solving a linear program in standard form, where the constraint matrix $A$ is $m \times n$, with $n \gg m \gg 1$. Such problems arise, for example, as the result of finely discretizing a semi-infinite program. The cost per iteration of typical primal-dual interior-point methods on such problems is $O(m^2n)$. We propose to reduce … Read more