The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

54 CHAPTER 5. BASIC API TUTORIAL
5.7 Integer optimization
An optimization problem where one or more of the variables are constrained to integer values is denoted
an integer optimization problem.
5.7.1 Example: Mixed integer linear optimization
In this section the example
maximize x 0 + 0.64x 1
subject to 50x 0 + 31x 1 ≤ 250,
3x 0 − 2x 1 ≥ − 4,
x 0 , x 1 ≥ 0 and integer
is used to demonstrate how to solve a problem with integer variables.
(5.10)
5.7.1.1 Source code
The example (5.10) is almost identical to a linear optimization problem except for some variables being
integer constrained. Therefore, only the specification of the integer constraints requires something new
compared to the linear optimization problem discussed previously. In MOSEK these constraints are
specified using the function Task.putvartype as shown in the code:
[ milo1.py ]
83 task.putvartypelist([ 0, 1 ],
84 [ mosek.variabletype.type int,
85 mosek.variabletype.type int ])
The complete source for the example is listed below.
1 ##
[ milo1.py ]
2 # Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
3 #
4 # File: milo1.py
5 #
6 # Purpose: Demonstrates how to solve a small mixed
7 # integer linear optimization problem using the MOSEK Python API.
8 ##
9
10 import sys
11
12 import mosek
13 # If numpy is installed, use that, otherwise use the
14 # Mosek’s array module.
15 try:
16 from numpy import array,zeros,ones
17 except ImportError:
18 from mosek.array import array, zeros, ones
19
20 # Since the actual value of Infinity is ignores, we define it solely