POLIPlibrary for polynomially constrained
 

This page describes the PIPformat  a file format for storing polynomially constraint mixedinteger programs. The syntax is a straightforward extension of the usual file format for storing linear programs (LPs) and mixedinteger programs (MIPs). Products are written using "*" and powers using "^" (hence these characters are not allowed in variable names). See below for an example.
<Program> = <Objective> ? <Constraints> ? <Bounds> ? <General> ? <Binary>? "End"
<Objective> = "Maximize""Minimize" <Label>? <Polynomial>?
<Label> = <Name>":"
<Polynomial> = <Monomial>*
<Monomial> = (<Number>"+""") (<Name>("^"<Integer>)?)*
<Constraints> = "Subject to" ( <Label> ? <Polynomial> ("<=""==""="">=") <Number> )*
<Bounds> = "Bounds" ( (("inf"<Number>) "<=")? <Name> (("<=") ("+inf""inf"<Number>))? )*
<General> = "General" <Name>*
<Binary> = "Binary" <Name>*
inf
or
inf
.inf
for
the upper bounds, except for binary variables for with the default values are 0 and 1,
respectively.The following are keywords:
The keywords are caseinsensitive.
Maximize
obj: x1 * x2 + 2 x2
Subject to
c1: 2 x1 + x2 x3 + 3 x4 <= 1
c2: 2 x1 +4 x4 == 30
c3: x2^3 == 2
c4: x4 = 1
Bounds
inf <= x1 <= 10
2 <= x2
x3 <= 2
Binary
x4
End
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