Additional notes
# Additional notes

Here are some brief notes about other things I said is lectures that
did not get into the notes. (This is mainly to help me remember next year
what I want to say or should have said.)

#### Lecture 1

- We write optimize, minimize, etc., with a z, for consistency with
international convention in the subject.
- I talked briefly about the concept of modelling. One can make
models of abstract entities (space, shape, symmetry) or physical
realities (motion, orbit, cost). Models are used to increase
understanding and for prediction. Often one wants to optimize control
of a system and modelling and optimization of a model can be a step
towards doing this.
- I mentioned the prevalence of optimization problems in the
biological sciences (e.g., as a result of natural selection many
organisms in nature appear to adopt behaviour that is the solution to
an optimization problem), physical sciences (e.g., some physical laws
can be represented as solutions to optimization problems: such as the
principle of minimum potential energy or least work), and social
sciences (where the desire to optimize in business and economics is
obvious).
- I described graphically the algebraic definition of a convex
function, and gave a mnemonic to distinguish between convex and
concave functions.
- I talked about the idea of local and global minimum and said that
convexity makes the distinction vanish.
- I described set partitioning and job scheduling problems and
rambled on a bit about the ideas of integer programming and
computational complexity.
- I said some things about my philosophy of lecturing and lecture
course design. I told students about the WWW site for the
course.
- Student questions:
- A student correctly noted after the lecture that there was a bit missing
from the definition of a convex set. It should
say "A set S is a convex set if given any x,y in
S then \lambda x+(1-\lambda)y is in S for all 0\leq \lambda\leq 1."

- I needed about 250 copies of the notes and had brought 260.

#### Lecture 2

Richard Weber ( r.r.weber@statslab.cam.ac.uk )

Last modified: Fri Apr 25 13:00:01 1997