Built-in Functions

Numerical Computation

Optimization

LinearProgramming

Usage

• 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 .

Notes

• 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.

Further Examples