Constrained positive deÖnite matrixes
Example
Solve the problemx 12 +x 22 +x 32 !min,x 1 +x 2 +x 3 = 1.
The Lagrangian is
L(x 1 ,x 2 ,x 3 ,λ)=x 12 +x 22 +x 32 +λ(x 1 +x 2 +x 3 1 ).
Obviouslyx 1 =x 2 =x 3 = 1 /3 is the solution.
A=
0
@
2 0 0
0 2 0
0 0 2
1
A,B= 1 1 1 ,H=
0
BB
@
0 1 1 1
1 2 0 0
1 0 2 0
1 0 0 2
1
CC
A
The determinant ofHis 12.