From: spellucci@mathematik.th-darmstadt.de (Peter Spellucci)
Newsgroups: sci.math.num-analysis
Subject: Re: Optimization problem
Date: 27 May 1998 10:35:37 GMT

In article <356b4ba0.1584771@news.polito.it>, darussol@DANYfreenet.hut.fi (Daniele Russolillo) writes:
snip
|> My problem is:
|> 
|> - I've found 3 scalar functions f,g,h
|> 
snip 
|> - Each Xi must be real and positive (I have also the possibility
|> to choose a range for each one)
|> 
|> - I should find a vector of 4 real elements (X1,X2,X3,X4) such that
|> function f is maximized and the g and h functions minimized, obviously
|> in the range I chose for each Xi. The system I'm studying is a real
|> thing, so I can't accept every value the algorithm finds for my
|> vector [X1,X2,X3,X4]

this is a so called multicriterion optimization problem.
obviously you have the constraints 
x_i >=0 , i=1,2,3,4
but you mention further restrictions, which you didn't state explicitly. 
multicriteria optimization problems are usually solved by so called 
scalarization, which means that you have minmize or maximize a weighted sum 
of the functions involved, as steven johnson already proposed. the selection 
of the weights however may quite heavily influence the solution and there exist
method which allow a adaptive selection of the weights during the solution
process.
the system NBI does exactly what you want and even better, is written in MATLAB.
you may access NBI through
http://plato.la.asu.edu/guide.html
hope this helps
peter