LinearProgramming
LinearProgramming[c,m,b]
finds a vector x that minimizes the quantity c.x subject to the constraints m.x≥b and x≥0.
LinearProgramming[c,m,{{b1,s1},{b2,s2},…}]
finds a vector x that minimizes c.x subject to x≥0 and linear constraints specified by the matrix m and the pairs {bi,si}. For each row mi of m, the corresponding constraint is mi.x≥bi if si==1, or mi.x==bi if si==0, or mi.x≤bi if si==-1.
LinearProgramming[c,m,b,l]
minimizes c.x subject to the constraints specified by m and b and x≥l.
LinearProgramming[c,m,b,{l1,l2,…}]
minimizes c.x subject to the constraints specified by m and b and xi≥li.
LinearProgramming[c,m,b,{{l1,u1},{l2,u2},…}]
minimizes c.x subject to the constraints specified by m and b and li≤xi≤ui.
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 xi to be in the domain domi.
Details and Options
- All entries in the vectors c and b and the matrix m must be real numbers.
- The bounds li and ui 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.
