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Documentation / Mathematica / Built-in Functions / Numerical Computation / Optimization /

LinearProgramming

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

FilledSmallSquare 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.

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

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

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

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

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

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

FilledSmallSquare LinearProgramming returns unevaluated if no solution can be found.

FilledSmallSquare 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.

FilledSmallSquare SparseArray objects can be used in LinearProgramming.

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

FilledSmallSquare See Section 3.9.8.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: NMinimize, Minimize.

FilledSmallSquare New in Version 2; modified in 5.0.

Further Examples