quadratic form under quadratic constraint
From: Tim (ads_at_theboohers.org)
Date: 02/07/05
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Date: 7 Feb 2005 15:43:07 -0800
I am trying to replicate some math results with matlab code and am not
getting agreement.
I have a quadratic program of the form
f(x)= x_1^2+x_2^2+x_3^2+...+x_n^2; (where x is a vector)
under the constraint
x'Qx=1 (where Q is symmetric positive definite)
Through the KKT conditions I get:
-inv(Q)*x=lambda*x and that lambda*=-x'*x;
Which means that the vector that corresponds to the minimum eigenvalue
in -inv(Q) should satisfy this equation. But a simple experiment
doesn't confirm this . . .
Given Q=
8 5 4
5 8 1
4 1 8
,none of the eigenvectors (v) of inv(Q) satisfy the property:
v'Qv=1
Any thoughts would be greatly appreciated,
Tim
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