Some of his math notation is not so
good.<p>His 22 slides on game theory go on and
on but are not clear on just the really
simple solution: It's just a really
simple linear programming problem.
Could knock it off on one slide, two
or three if wanted to be verbose.
I did that when I taught linear programming
in college and an MBA program.<p>More generally, a large fraction of these
topics and a larger fraction of the
more basic tools are what was
long called the <i>mathematical sciences</i>,
where generally the work was done
more carefully, and, in particular, the
mathematics of operations research
along with, sure,
and pure and applied statistics.<p>He ends up with genetic algorithms and
simulated annealing. Gee,
I encountered such a problem only once:
Some guys had a resource allocation
problem and formulated it as a
0-1 integer linear program with
40,000 constraints and 600,000
variables. They had tried simulated
annealing, ran for days, and
stopped with results
with objective function value
of unknown distance from the
optimal value.<p>I saw an approach via Lagrangian
relaxation, which really needs
most of a nice course in optimization,
wrote some software, and got
a feasible solution with objective
function value guaranteed to be
within 0.025% of optimality.
My software ran for 905 seconds
on an old 90 MHz PC.<p>For the bound of 0.025%,
Lagrangian relaxation has,
on the optimal value of the objective
function,
both a lower bound and an upper bound
and, during the <i>relaxation</i>,
lowers the upper bound and raises
the lower bound. When the
two bounds are close enough for
the context, then take the
best feasible solution so far
and call the work done.<p>I'd type in the basics here except
I'd really need TeX.<p>The resource allocation problem
was optimization, just optimization,
and needed just some of what had
long been known in optimization.
Simulated annealing didn't look
very good, and it wasn't.<p>Optimization, going back to
mathematical programming,
unconstrained, constrained,
the Kuhn-Tucker conditions,
linear programming, network linear
programming,
integer programming,
dynamic programming, etc. were
well developed fields starting
in the late 1940s with
a lot of work rock solid by
1980.<p>Good work has come from Princeton,
Johns Hopkins, Cornell,
Waterloo, Georgia Tech, University
of Washington, etc.