From c2fortin@barrow.uwaterloo.ca Fri Feb 19 10:44:09 1999
Date: Wed, 10 Feb 1999 09:44:14 -0500 (EST)
From: Charles Fortin <c2fortin@barrow.uwaterloo.ca>


--In number 4a), some people argued that f was coercive.  It is not the
case. One can see for example that

f(w,0) = w^3 ,and as w goes to -infinity (minus infinity), i.e. the norm
of (w,0) goes to infinity, f goes to -infinity as well.  Therefore, f is
NOT coercive.

-- I have found in several cases the following:

"If the leading principal minors of A are greater or equal to 0, than A is
positive semidefinite".

This is not true.

-- In 4a) some people also said:

" If there exist a global min for f, then the Hessian of f is positive
semidefinite"

This is not true. It is only true at the global minimum (or at a local
minimum).

-- People who lost points in number 5 should look at the right answer.
Most people didn't do very well on this problem.

-- In 6c), one of the keys for this exercise was to see that 

A positive definite implies that A is invertible.

-- In number 7, the expression "the minimizer" refered to the global
minimizer.