constrained optimalisation with f(x,y) polynomals

[ivran]

hi guys,

I'm having a big problem using scilab and some basic math. I would really
appreciate some help with it 'cause i'm stuck - Consider the following
problem:

2 polynomials, each describing a coordinate on its own. Together they form a
2D - f(x1,x2) surface which can have 2 - or more - maximums on a certain
spot. 

f(x1) = p1 =                                         2             3            
4             5             6  
    55.044419 - 1.3570362x1 + 0.0162766x1 - 0.0001039x1 + 0.0000004x1 -
4.592D-10x1 + 1.854D-13x1   

f(x2) = p2 =                        2             3             4            
5             6  
    560.98702 - 23.76471x2 + 0.2962816x2 - 0.0009662x2 + 0.0000013x2 -
8.576D-10x2 + 2.074D-13x2   

I have two problems here:

1) Does anyone know how to combine these 1D polynomials to a 2D polynomial?
f(x1, x2) = px1x2 = p1 + p2
...won't work. How can I solve this without overloading the '+' method?

2) suppose I *could* combine these 2 functions:
f(x1, x2) = ...x1 + ...x2 + ...x1^n + ..x2^n
how can I find the maximum values of this function?, given the following
constraints:
x1.x2 <= 1024
x1.x2 >= 0

I'm (a little) familiar with Lagrange and the scilab procedures regarding
this topic... but it would be very helpful if someone could post me a
example of this (or something close related) 2D constrained optimization
problem.

I'm really stuck at this... could you point me in the right direction? ..tkx
in advance!!

Iwein
 





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