POLIP

This page describes the PIP-format - a file format for storing polynomially constraint mixed-integer programs. The syntax is a straight-forward extension of the usual file format for storing linear programs (LPs) and mixed-integer programs (MIPs). Products are written using "*" and powers using "^" (hence these characters are not allowed in variable names). See below for an example.

Token Description

<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>*

Additional Requirements

• All tokens must be separated by white-spaces.
• Names/labels can contain at most 255 characters.
• Name/labels have to consist of the following characters: a-z, A-Z, 0-9, "!", "#", "$", "%", "&", ";", "?", "@", "_". They cannot start with a number.
• The maximal length of a line is 65536.
• Everything after a backslash "\" is ignored until the end of the current line. Empty lines are ignored.
• Each constraint has to begin on a new line.
• Objective, Constraints, Bounds, and integrality conditions can be distributed over several lines.
• No brackets/parenthesis are allowed.
• Lower or upper bounds can be skipped or replaced by -inf or inf.
• Default value for the lower bounds of variables is 0 and inf for the upper bounds, except for binary variables for with the default values are 0 and 1, respectively.
• Variables in monomials have to be separated by white-spaces or "*".
• The program has to end with "End".

Keywords

The following are keywords:

• Maximize/Max
• Minimize/Min
• Subject to/st/s.t.
• Bounds
• General
• Binary
• inf
• End

The keywords are case-insensitive.

Example

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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