I have an expression that I have to minimize. The expression is a sum of piecewise functions each function depending on 3 variables.

Let's say Si(ai,bi,ci) is my function, i goes from 1 to N. The sum that I try to minimize is The sum of all Si functions (i from 1 to N).

Is the first derivative an option in this case? We're talking about 3*N variables (ai,bi,ci where i is from 1 to N).



  • $\begingroup$ It sounds like the variables are independent, and so the minimum of the sum is the sum of the minima, in which case find the minimum for each function i, and then sum the N minima. Gerhard "Sometimes The Obvious Is Simple" Paseman, 2011.02.24 $\endgroup$ – Gerhard Paseman Feb 24 '11 at 10:21

Unless your functions have a very special structure (convex? independent as in @Gerhard's comment? smooth?) I (a) don't see how you can differentiate [you say your functions are piecewise], and (b) don't see what good it would do you if you could (you might find some local minimum, if the gradient had some very simple form, but would not know it was a global minimum).


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