Help!!! constrained minimization


Tommy
03-29-2006, 03:50 PM
To everyone:

My problem is to minimize the following equation:
f=SUM[m(i)-sum(aj*exp(-λj*ti))]**2
i=1,2....100
j=1,2....6

M(i) is the measured points we already know.
aj and λj are variables ---- 12 unknown variables together.
ti is the time constant at point i ----we already know the values.

Constraints:
sum(aj)=1 (j=1,2....6)
0<aj<1
0< λ1 < λ2 < λ3 < λ4 < λ5< λ6

My purpose:
----To find the values of aj and λj (j=0,1…6) which fit the equation very well.

Thanks for your help.