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

102 CHAPTER 8. A CASE STUDY
Variable Length Offset
x n 1
s 1 n+1
t n n+2
Figure 8.1: Storage layout of the ˆx variable.
c = [ ]
µ T 0 0 T
[ n,1 ,
]
e
T
0 0
A =
n,1
G T ,
0 n,1 − I n
l c = [ ]
w + e T x 0 0 0 T
1,n ,
u c = [ ]
w + e T x 0 0 0 T
1,n ,
l x = [ ]
0 1,n γ − ∞ T n,1 ,
u x = [ ]
∞ n,1 γ ∞ T n,1 .
The next step is to consider how the columns of A is defined. The following pseudo code
for
j = 1 : n
ˆx j = x j
A 1,j = 1.0
A 2:(n+1),j = G T j,1:n
ˆx n+1 = s
for
show how to construct each column of A.
j = 1 : n
ˆx n+1+j = t j
A n+1+j,n+1+j = −1.0
In the above discussion index origin 1 is employed, i.e., the first position in a vector is 1. The Python
programming language employs 0 as index origin and that should be kept in mind when reading the
example code.
1 """
2 File : case portfolio 1.py
3
[ case portfolio 1.py ]
4 Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
5
6 Description : Implements a basic portfolio optimization model.
7 """
8
10
9 import mosek
11 try:
12 from numpy import zeros
13 except ImportError:
14 from mosek.array import zeros