Presolve an assembled LP

Exact reductions applied before the matrix is handed to a solver. The one step implemented, "doubletons", removes every equality row of the form a * x + b * y = 0 together with column x, substituting x = c * y (c = -b / a) into the rest of the matrix, the objective and y's bounds. Integer columns are never eliminated. The reduced LP solves to the same optimum; read_mps_solution() restores the eliminated columns from the table kept in the result.

Usage

lp_presolve(
  lp,
  steps = "doubletons",
  max_pass = 50L,
  tol = 1e-12,
  verbose = FALSE
)

Arguments

lp

An LP from model_to_lp().

steps

Reductions to apply; "doubletons" is the only one so far.

max_pass

Maximum number of passes; chains need one pass per link.

tol

Entries smaller than this in absolute value after substitution are dropped (exact cancellations that floating point leaves behind).

verbose

Logical; report each pass.

Value

The LP with A, obj and the bounds reduced. col_index and row_index stay complete and gain jred / ired, the position of each kept column / row in the reduced LP (NA when eliminated); eliminated lists the removed columns (col, ref, coef, pass, positions in the full index) so that value[col] = coef * value[ref], applied from the last pass to the first.