First off, I'm not a mathematican, I just like to read different kind of books because they are interesting, and I think this is a great book. Programming is very new to me and am working my way through it, but my main question, is that I would like to run a multi variable optimization of the quadratic form and I need to incorporate constraints such that all the input variables are greater than or equal to zero and also that they must add up to one. It is an asset allocation problem. I'm 54 years old and take things a little slower than I used to, but I've been trying to work my way through the code and have been having problems, I was looking specifically at the amoeba program, but any help would be appreciated, I would just like to finish it once and for all! Thank you again,
Steve

Bravo, Steve, for your perserverence and obvious broad interests!
I think that the problem you are talking about is formally called "quadratic programming with linear constraints". When I do a quick Google search on this, I find a nice site at http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/qprog/ that has links to some programming packages for this. Specialized methods will be MUCH more efficient and reliable than AMOEBA or some other general minimizer (which will also have a hard time with the constraints).
Good luck!

Hello,
You could use the method of Lagrange multipliers for maxima and minima. See, e.g., Schaum's Outline Series "Theory and Problems of Advanced Calculus" by Murray R. Spiegel (1963, 1974,...), including 925 solved problems, Ch. 8. Then you could program with "Maple", "Mathematica"...
Best regards, JPR

Originally posted by JP_Rivera
Hello,
You could use the method of Lagrange multipliers for maxima and minima. See, e.g., Schaum's Outline Series "Theory and Problems of Advanced Calculus" by Murray R. Spiegel (1963, 1974,...), including 925 solved problems, Ch. 8. Then you could program with "Maple", "Mathematica"...
Best regards, JPR

Hi JP_rivera: i have this Schaum book and got quite interested in the technique you describe. My qn is that the Schaum book only seems to alow one factor - but can i use 2 or 3 factors (constraints) - how would i proceed then?
Thanks , best wishes.... Robin:)

guys:

to answer my own question: can the method of "Lagrange Multiplier" be applied to more than one constraint?

the answer is YES it can- see the book by CH Edwards Jr
"Advanced Calculus of Several Variables" Ch 5 - Manifolds and Lagrange Multipliers, i stress that Multiplier is plural. There are several examples starting after theorem 5.8 - the language and notation is obscure, but perhaps this method could be used when needed - elsewhere i have seen caveats against using the Lagrange Multiplier(s) method namely: "bordered Hessian determinants" may describe conditions of sufficency - about which i have not a clue, but try anyway---- !
Robin
:rolleyes: