Additional notes 1995
Additional notes 1995
Here are some brief notes about other things I said is lectures that
did not get into the notes. (This is partly to help me remember next year
what I want to say or should have said.)
Lecture 1
There were about 30 students present.
I showed overhead slides of the www pages for the course.
I drew a little diagram to illustrate the idea of optimization
in stages.
I recommended that students attempt question 1 on the examples sheet
prior to the next lecture.
Unfortunately, it was not possible to move the lecture from Saturday to
a weekday slot, since many of the students were doing other courses
at the same time.
Lecture 2
We arranged that I would *not* lecture on Sat 28 October and Wed 1
November. These will be replaced with lectures on Monday 16 and 23
October at 3pm. I apologise to the one person who is not going to be able
to make that time.
I asked students to sign a list if they wished supervision. There were
18 who signed.
There is about 5 minutes too much material in this lecture
for comfort. It's hard to see what to eliminate, since all four
examples are quite nice and standard examples for this sort of course.
But this is something for me to think about for next year. Maybe
something could go into Lecture 3, since that lecture is much shorter.
Due to revising last year's notes in order to make the
exposition of Example 2.4 rather cleaner, (which it now is), I introduced
a small error into the notes. See
corrections.
Lecture 3
I handed out arrangements for supervisions.
When I said that conditions D, N or P were sufficient to guarantee that
the limit lim_{s\rightarrow\infty} F_s(\pi,x) exists because of
montone convergence, a student asked how we know this is bounded above.
We don't. But we allow \infty as a possible value of the limit.
I included a digression on Robert Aumann's
repeated game with partial information.
Lecture 4
I included a digression about the `find the oldest' problem.
Lecture 5
I included a digression about the Palasti conjecture problem.
A student asked afterwards "what policy is used in defining
the set S (for the one-step-look-ahead rule)?" The point is that this
set is defined by comparing the cost of stopping now to going on
and then stopping at the next step. There is nothing more to say about
policy at this point.
I handed out summary sheet 1.
Lecture 6
I explained Section 6.1 using $\lambda^*$ rather than $\lambda$ for the
infimal average cost. This ties in better with the was Theorem
6.1 is stated.
I included a digression about a self-organizing system.
Lecture 7
I handed out Examples Sheet 2.
I was pressed for time to prepare a relevant digression for this
lecture, but I included a humourous digression on black magic and
photocopiers.
A student asked about the meaning of the matrix $N$ on page 33.
The point is that $N_{ij}=E\epsilon_i\epsilon_j$, i.e., the covariance
of those two components of $\epsilon$.
Lecture 8
I included a digression about the instability of the aloha protocol.
A student pointed out an error where u_0 and u_1 are interchanged
in the second example on page 36.
See corrections.
If I am going to "waste" 5 minutes on a digression, then the
lecture is a bit full. It would be possible to abbreviate the stuff
about disturbances and tracking, or merge their treatment into a
single section that could be dealt with more briefly by using an
overhead to display the equations. Clearly, students are not expected
to learn these equations, simply to have an appreciation of the sort
of wrinkles that can be added to the simple LQ model.
Lecture 9
My digression today was a brief reporting of some of the cute anecdotes
about risk that I had heard from Ralph Keeney at the New Orleans INFORMS
conference.
There is really too much in this lecture. I did not have time to
go through the Theorem 9.3 . Next year I should probably delete this.
The discussion of the infinite horizon case is certainly not
essential. Maybe I can figure out a way to simplify the proof.
Lecture 10
I did a digression about the problem of searching for a moving
object.
Lecture 11
This plan for lecture is pretty full. I didn't have time to work
through the example in the final section. All in all, the content of
Lectures 7-11 should be reduced next year, probably by deleting stuff
about the infinite horizon limit.
Lecture 12
I did a digression about the Lady's Nylon
Stocking Problem.
A student asked why the optimal solution to the fishing problem
isn't always to fish at an equilibrium point $x^*$ such that
$u=a(x^*)=\max_x a(x)$. The point is that the discounting gives
incentive to sacrifice long term gain for short term gain and this
causes the equilibrium to settle at a smaller point that $x^*$. This
point is smaller the larger the value of $\alpha$. If $\alpha>a'(0)$
then it is optimal to exhaust the fish population entirely.
The fish harvesting example will be less ambiguous with regard to
the above point if I redraw the picture so that $u_{max}>\max_x a(x)$.
In this case, $u=u_{max}$ always causes a strict decrease in the
population.
Lecture 13
Nothing special. Just the lecture as in notes.
Lecture 14
I added a digression about Richard Steinberg's optimization model
for pulsed advertising expenditure.
Lecture 15
I gave students time to fill in the course questionnaire.
Lecture 16
I briefly talked about the rendezvous problem.
Return to the Optimization and Control course page.
Richard Weber ( r.r.weber@statslab.cam.ac.uk )
Last change to this page: 21 August, 1996.