... expressed in Theorem 2, Section 5.6.
15 .9 SEMIDEFINITE PROGRAMMING
Semidefinite programming (SDP) is a natural extension of linear programming. In
linear programming, the variables form a vector which ... satisfying the first-
order conditions for problems when fx and g
i
x are not generally convex
functions.
Quadratic Programming
Let fx = 1 /2 x
T
Qx +c
T
x and g...
... hypothesis both g
k
and Qd
k
belong to g
0
Qg
0
Q
k +1
g
0
, the
first by (a) and the second by (b). Thus g
k +1
∈ g
0
Qg
0
Q
k +1
g
0
. Furthermore
g
k +1
g
0
Qg
0
Q
k
g
0
... g
0
g
1
g
k
= g
0
Qg
0
Q
k
g
0
b) d
0
d
1
d
k
= g
0
Qg
0
Q
k
g
0
c) d
T
k
Qd
i
=0 for i k 1
d)
k
=g
T
k
g
k...
... identity
A
1
A
2
A
T
2
A
3
1
=
A
1
−A
2
A
1
3
A
T
2
1
−A
1
−A
2
A
1
3
A
T
2
A
2
A
1
3
−A
1
3
A
T
2
A
1
−A
2
A
1
3
A
T
2
1
A
3
−A
T
2
A
1
1
A
2
1
(29 )
Using the fact that A
1
3
c → 0 gives the result.
To ... 388565
3 8 24 388563
5 3 15 388563
7 3 21 388563
c = 20 0
⎧
⎪
⎪
⎨
⎪
⎪
⎩
1 23 0
∗
23 0 488607
3...