Tuesday, July 14, 2015

monotonic transformations

From: lp_solve@yahoogroups.com
To: lp_solve@yahoogroups.com
Date: Thu, 9 Jul 2015 00:32:47 -0700
Subject: [lp_solve] C# to set the object with the form of square

Could LP set the object in a form of square? Just like this :
min: Q^2

If we have Q≥0 then just use MIN Q. We can apply a monotonic function. I have used this trick a lot in the context of minimizing distances. Instead of image

we can keep things quadratic by using

image

This got rid of a nasty square root and this allowed us use quadratic solvers.

Back to the original problem where we want to remove a square. What if we don’t know in advance that Q≥0? Then we can solve two problems:

image

and pick the best one.

The suggested solution in the thread: “Have a look into piecewise linear approximations” is at least much overkill.