[Antichron]

It has been almost two years since I read Chiang and Simon/Blume, so if I say something wrong, please forgive me.

Chiang is a bit dated (and thus a bit simplistic), but still seems somewhat relevant. There is a lot of emphasis on second order conditions, which in my experience are not stressed much in the first year program. Simon/Blume is a nice book with a decent coverage of a sizable chunk of the relevant topics. Neither book delves into many of the linear algebra topics that will be useful for econometrics nor into dynamic programming, which is quite widespread in macro.

De la Fuente is an awesome book, but it might be a little too much to study on one's own. It is very comprehensive, detailed, and has nice notation, but it is a bit on the difficult side, where as both Chiang and Simon/Blume are very accessible.

Another book that I would highly recommend is Dixit's Optimization. It is a think book (~150 pages?), and it covers all the optimization theory you are likely to encounter in your first year. It does so from a different perspective than most other texts, so it will be both a good review and you will learn new things. In addition, it is significantly cheaper than the three books you mentioned. It does have a section on dynamic programming, but I haven't read it, so I don't know how good it is. It does NOT cover any topics relevant to econometrics, however. (Well, optimization is very relevant for extremum estimators, but that will come later in the year.)