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

100 CHAPTER 8. A CASE STUDY
maximize µ T x
subject to e T x = w + e T x 0 ,
[γ; G T x] ∈ Q n+1 ,
x ≥ 0,
which is a conic quadratic optimization problem that can easily be solved using MOSEK.
Subsequently we will use the example data
(8.3)
and
This implies
⎡
Σ = 0.1 ⎣
⎡
µ = ⎣
0.1073
0.0737
0.0627
⎤
⎦
0.2778 0.0387 0.0021
0.0387 0.1112 − 0.0020
0.0021 − 0.0020 0.0115
⎤
⎦
⎡
G T = √ 0.1 ⎣
using 5 figures of accuracy. Moreover, let
0.5271 0.0734 0.0040
0 0.3253 − 0.0070
0 0 0.1069
⎤
⎦
and
⎡
x 0 = ⎣
0.0
0.0
0.0
⎤
⎦
w = 1.0.
The data has been taken from [5].
8.1.2.1 Why a conic formulation?
The problem (8.1) is a convex quadratically constrained optimization problems that can be solved
directly using MOSEK, then why reformulate it as a conic quadratic optimization problem? The main
reason for choosing a conic model is that it is more robust and usually leads to a shorter solution times.
For instance it is not always easy to determine whether the Q matrix in (8.1) is positive semidefinite
due to the presence of rounding errors. It is also very easy to make a mistake so Q becomes indefinite.
These causes of problems are completely eliminated in the conic formulation.
Moreover, observe the constraint