LinearProgramming

LinearProgramming[c, m, b] finds a vector x which minimizes the quantity c.x subject to the constraints and .

LinearProgramming[c, m, , , , , ... ] finds a vector x which minimizes c.x subject to and linear constraints specified by the matrix m and the pairs , . For each row of m, the corresponding constraint is . x if == 1, or . x == if == 0, or . x if == -1.

LinearProgramming[c, m, b, l] minimizes c.x subject to the constraints specified by m and b and .

LinearProgramming[c, m, b, , , ... ] minimizes c.x subject to the constraints specified by m and b and .

LinearProgramming[c, m, b, , , , , ... ] minimizes c.x subject to the constraints specified by m and b and .

All entries in the vectors c and b and the matrix m must be real numbers.

The bounds and must be real numbers or Infinity or -Infinity.

LinearProgramming gives exact rational number results if its input is exact.

LinearProgramming returns unevaluated if no solution can be found.

LinearProgramming finds approximate numerical results if its input contains approximate numbers. The option Tolerance specifies the tolerance to be used for internal comparisons. The default is Tolerance->Automatic, which does exact comparisons for exact numbers, and uses tolerance for approximate numbers.

SparseArray objects can be used in LinearProgramming.

With Method->"InteriorPoint", LinearProgramming uses interior point methods.

See Section 3.9.8.

Implementation Notes: see Section A.9.4.

See also: NMinimize, Minimize.

New in Version 2; modified in 5.0.

Further Examples