LinearProgramming

LinearProgramming[c, m, b]
finds a vector x that minimizes the quantity subject to the constraints and x≥0.

LinearProgramming[c, m, {{b1, s1}, {b2, s2}, ...}]
finds a vector x that minimizes subject to x≥0 and linear constraints specified by the matrix m and the pairs . For each row of m, the corresponding constraint is if , or if , or if .

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

LinearProgramming[c, m, b, {l1, l2, ...}]
minimizes subject to the constraints specified by m and b and .

LinearProgramming[c, m, b, {{l1, u1}, {l2, u2}, ...}]
minimizes subject to the constraints specified by m and b and .

LinearProgramming[c, m, b, lu, dom]
takes the elements of x to be in the domain dom, either Reals or Integers.

LinearProgramming[c, m, b, lu, {dom1, dom2, ...}]
takes to be in the domain .

Details and OptionsDetails and Options

  • 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.
  • None is equivalent to specifying no bounds.
  • LinearProgramming gives exact rational number or integer results if its input consists of exact rational numbers.
  • 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.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

Minimize , subject to constraint and implicit non-negative constraints:

In[1]:=
Click for copyable input
Out[1]=

Solve the problem with equality constraint and implicit non-negative constraints:

In[2]:=
Click for copyable input
Out[2]=

Solve the problem with equality constraint and implicit non-negative constraints:

In[3]:=
Click for copyable input
Out[3]=
New in 2 | Last modified in 6
New to Mathematica? Find your learning path »
Have a question? Ask support »