Constrained positive deÖnite matrixes
Now letx 1 = 0 ,x 2 = 1 ,x 3 =0 andλ= 1 ,which solves the equations.H=
0
BB
@
0 0 2 0
0 4 0 0
2 0 0 0
0 0 0 0
1
CC
A.
The determinant is 0.The problem comes from the fact that( 0 , 1 , 0 )is not
a isolated local minimum asx 1 = 0 ,x 22 +x 32 =1 are all minimal solutions.