SYLLABUS (=pensum):
The preliminary syllabus is the union of
(i) those topics that are lectured (see lecture notes + "A mini-introduction to convexity"), and
(ii) the following from Vanderbei:
- Chapter 1-6: all
- Chapter 7: 7.1
- Chapter 11: 11.1-11.3
- Chapter 12: 12.4
- Chapter 14 (in 2.ed.: chapter 13): all sections except 14.5
- Chapter 15: 15.3 (shortest paths)
- Chapter 17: all
(Here, for instance, 11.1-11.3 means, 11.1, 11.2 and 11.3.) As you will (be glad to) see, the intersection between (i) and (ii) above is huge!
We use the book R.Vanderbei, "Linear programming: fundations and extensions". Third Ed., Springer (2008) (or you may use Second edition, Kluwer (2001): the only essential difference is a new chapter 13 on financial applications). In addition we use the notes G.Dahl, "A mini-introduction to convexity" (2004), which may be found on the course webpage.
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NOT SYLLABUS:
Additional reading: these are some suggestions if you want to read more (outside the syllabus) in this and related areas:
- In Vanderbei: interior point methods, a very readable presentation is found in Chapter 17, 18 and 19.
- In Vanderbei, Chapter 13 is an interesting presentation of applications in finance: portfolio optimization and option pricing.
- In Vanderbei, Extensions (Part 4): the Markowitz model (Chapter 24) and quadratic programming, which extends into convex optimization (Chapter 25). Integer programming is a large area with active research and many applications; a brief introduction is Chapter 23 in Vanderbei.
- A recommended book in comvex optimization is Boyd, Vandenberghe, "Convex Optimization", Cambridge, 2004.
- A well-written and popular book in network optimization is Ahuja, Magnanti, Orlin, "Network Flows: theory , algorithms and applications", Prentice-Hall, 1993.
- Another good book (similar topics and approach as Vanderbei) is V. Chvatal, "Linear programming", W.H.Freeman, 1983; it contains a few other areas than Vanderbei.
- In (i) convexity and (ii) nonlinear optimization, there are several excellent books, just ask for recommendations.