March 2010
Intermediate to advanced
238 pages
5h 59m
English
Content preview from Portfolio Optimization
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122 A QP Solution Algorithm Chap. 6
Step 3.2: u
1
= (0, 0, −8, −2)
′
,
(u
1
)
3
= min { 0, 0, −8, −2 } = −8, k = 3,
K
1
= { 4 }, A
1
= [ 0 1 ] , H
1
=
2 0 0
0 2 1
0 1 0
,
j = 1.
Iteration
1
Step 1: Solving H
1
s
1
v
1
=
g
1
0
gives s
1
=
−4
0
and
v
1
= [ 2 ] .
Step 2: ˆσ
1
= min
−3
−4
, −, −, −
=
3
4
, l = 1,
σ
1
= min
3
4
, 1
=
3
4
.
Step 3: x
2
=
1
3
−
3
4
−4
0
=
4
3
, g
2
=
−2
2
,
f(x
2
) = −27. Transfer to Step 3.1.
Step 3.1: K
2
= { 4, 1 }, A
2
=
0 1
1 0
,
H
2
=
2 0 0 1
0 2 1 0
0 1 0 0
1 0 0 0
, j = 2.
Iteration
2
Step 1: Solving H
2
s
2
v
2
=
g
2
0
gives s
2
=
0
0
and
Sec. 6.1 QPSolver: A QP Solution Algorithm 12 3
v
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