It's some quite precisely done mathematics
with one theorem with a careful proof
and some smaller results also proved.
And there's some impressive computational
experience. We're talking a 0-1 integer
linear program with 40,000 constraints and
600,000 variables -- that is an example of
a problem in NP-complete. That we could
do anything with such a problem is a bit
amazing.
That we can apply non-linear optimization
to a problem in discrete or combinatorial
optimization, that is, 0-1, is curious,
in this case powerful, and, thus,
generally welcome.
That we are making good progress with
Lagrange multipliers without
taking any derivatives, e.g., as in
the Kuhn-Tucker conditions,
is also
curious -- so, this is not your
father's Lagrange multipliers.
And I proved Everett's theorem: That's
a famous result, and quite useful,
much more useful than difficult to prove,
in
a wide range of resource allocation problems.
And Everett is a famous guy, a physics
Ph.D. under J. Wheeler (one of the
main guys in relativity theory, in the world)
at Princeton
and the first guy to expound on the
many worlds (parallel universes)
interpretation of quantum
mechanics. Everett thought that his
result was worth publishing, and what
I wrote is more general and more powerful.
Simulated annealing is famous;
that some non-linear duality theory
and Lagrangian relaxation totally blew
away simulated annealing on an impressive
practical problem should also be of
interest.
That it is possible to get better
performance using central cutting planes
is actually not very well known.
Also I covered the mathematics
in essentially full detail (everything
important and not obvious, proved)
starting with next to nothing,
gave a description of an algorithm
that is ready to code (it's basically
just what I did code from successfully)
and also
the impressive computational experience,
all in just that one post.
Simulated
annealing is rarely described so
carefully, and it doesn't provide bounds
on optimality, that is, we don't know
when to stop.
As I illustrated, my work
provides bounds which commonly in practice
provide a good stopping criterion.
Simulated annealing is sometimes regarded
as part of computer science; well, my post
shows something that sometimes is better
and from applied mathematics.
Actually, the mathematics for such
optimization problems is a well-developed
and deep field; try to do much in
optimization, and really should consider
some of the mathematics, e.g., what
I posted.
Oh, by the way, my Ph.D. is in
stochastic optimal control, and
I've published peer-reviewed original
research on non-linear optimization,
e.g., some deep details about the
Kuhn-Tucker conditions.
My professors included some of the
best people in the world in optimization.
The Chair of my Ph.D. orals committee
is a Member, US National Academy of
Engineering and was a student of
A. Tucker of the Kuhn-Tucker conditions --
Kuhn and Tucker were both at Princeton.
You might let us know where you found the
part with the "opinion"?
Supposedly HN likes only really highly
relevant comments and viciously down votes
anything else, especially jokes, and
everything else, no matter how serious or
relevant, by the user they are down voting.
Here I've been viciously, bitterly, attacked
by some people apparently totally pissed off
at me for next to nothing, a
simple contribution follow up,
a famous quote from the movie Casablanca,
as a follow up
to a post
with the earlier part of that famous
quote from Casablanca.
So, my post on Lagrangian relaxation, that took
much of an afternoon to write, and with careful
theorems and proofs, with some material not
so easy to find, especially in such a succinct,
careful, and complete
form, and that stands to be of high interest
to anyone interested in simulated annealing,
gets downvoted -- a joke about my post does not,
and my response to the joke post does.
HN is getting to be a very nasty place,
not nearly as nice as, say, Reddit. Sorry
HN.
Sam,
PG, you've got a problem. You need to look
at your log files and find who has decided
to hate me and down vote anything I post,
no matter what I write.
My post on Lagrangian relaxation is right up
there in quality with some of the best
expository writing in optimization, and I
know enough to know. That I get down voted
is the problem of HN, not my post. In the
past few days, the bitter, hostile, personal
attacks on me have cost me 70+ points,
no doubt to the great pleasure of
my attackers. I'm being bitterly attacked
personally, for no good reason, and now
independent of what I post.
