Unconstrained local su¢ cient conditions
Lemma
If xTHx is a positive deÖnite quadratic form onRnthen there is anα> 0
such that
xTHxαkxk^2.
Letα>0 be the minimum ofxTHxover the compact setkxk= 1.
Obviously
x
kxk
T
H x
kxk
α> 0
which implies the lemma.