🚀 go-pugleaf

Hi,

  a question about "scaling" of variables in optimization problems. A
commonly used approach is the linear trasformation:

             x = D*y + c; {x} - original vars., {y} - transformed vars.

suppose an element x_j lies in [a_j,b_j]. Then we have

         D(j,j) = 0.5*(b_j - a_j) and c(j) = 0.5*(b_j + a_j)
      
This ensures that  -1 <= y_j <= +1 .

  In my particular application, I have a range such as [1,1e5]. If I
use the above procedure, it turns out that values in the range [1,1e4]
(approximately) are "compressed" into [-1,-0.8]. This would be a
problem if say the gradients are computed by finite differences.

Another scaling method would be y = log10(x). This avoids the
"compression" problem but gradient computations would be screwed up
(if you use a canned code like I am).

Does anybody have experiences with scaling problems like this?
Any suggestions and pointers would be much appreciated. Thanks.

-sriram (a novice in the practicalities of optimization)

-------------------------------------------------------------------------------
Sriram Srinivasan                        ss4i@kelvin.seas.virginia.edu
Dept. of Mech. and Aero. Engg
Univ. of Virginia
-------------------------------------------------------------------------------