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

Return to the Optimization IB course page.

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