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

5.5. QUADRATIC OPTIMIZATION 49
5.5.2 Example: Quadratic constraints
In this section describes how to solve a problem with quadratic constraints. Please note that quadratic
constraints are subject to the convexity requirement (5.8).
Consider the problem:
This is equivalent to
minimize x 2 1 + 0.1x 2 2 + x 2 3 − x 1 x 3 − x 2
subject to 1 ≤ x 1 + x 2 + x 3 − x 2 1 − x 2 2 − 0.1x 2 3 + 0.2x 1 x 3 ,
x ≥ 0.
where
⎡
Q o = ⎣
minimize 1/2x T Q o x + c T x
subject to 1/2x T Q 0 x + Ax ≥ b,
2 0 − 1
0 0.2 0
− 1 0 2
Q 0 =
⎤
⎡
⎦ , c = ⎣
⎡
0
− 1
0
⎤
⎣ − 2 0 0.2
0 − 2 0
0.2 0 − 0.2
⎦ , A = [ 1 1 1 ] , b = 1.
⎤
⎦ .
1 #
5.5.2.1 Source code
[ qcqo1.py ]
2 # Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
3 #
4 # File: qcqo1.py
5 #
6 # Purpose: Demonstrates how to solve small linear
7 # 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
21 # for symbolic purposes:
22 inf = 0.0