LinearProgramming

LinearProgramming[c,m,b]
finds a vector x that minimizes the quantity subject to the constraints and x0.

LinearProgramming[c,m,{{b1,s1},{b2,s2},}]
finds a vector x that minimizes subject to x0 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]=
Introduced in 1991
(2.0)
| Updated in 2007
(6.0)