Syllabus/achievement requirements

The preliminary syllabus is the union of

(i) those topics that are lectured (see lecture notes + "A mini-introduction to convexity"+ "Lagrange duality"), 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): it may be read for free, see http://link.springer.com/book/10.1007%2F978-0-387-74388-2 . (You may use the Fourth edition, but some small differences exist). In addition we use the notes G.Dahl, "A mini-introduction to convexity" (2004), which may be found here /studier/emner/matnat/math/MAT-INF3100/v14/convmat-inf3100.pdf

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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.