0
$\begingroup$

I would like to minimize a simple function that is defined only for a certain range of the independent variable. The function has only one minimum. To illustrate, let's take a parabola defined for $x\in [17,22]$. In mathematica, I tried

NMinimize[
 Piecewise[{{0.01 (x - 19.5)^2 + 16, x > 17 && x < 22}, {Exp[10000], 
    True}}], x, Method -> "DifferentialEvolution"]
(* {8.80681822566*10^4342, {x -> -6.96782}} *)

The result is apparently nonsense. It doesn't seem to matter which Method I use. I guess the issue is the way how I define the forbidden points (by setting their values to Exp[10000]). Is there a robust way to exclude points or generally speaking a more robust way to find the minimum of a function with limited domain, knowing that the function has definitely just one minimum?

$\endgroup$
3
  • 1
    $\begingroup$ You have to add a constraint: NMinimize[{func, 17 < x < 22}, x]. $\endgroup$ Oct 5, 2016 at 19:33
  • $\begingroup$ To see why giving NMinimize some notion of where to look is needed, examine the x's that are tested in your code: ListPlot@Last@Reap@NMinimize[Piecewise[{{0.01 (x - 19.5)^2 + 16, x > 17 && x < 22}, {Exp[10000], True}}], x, Method -> "DifferentialEvolution", EvaluationMonitor :> Sow[x]] -- the x's appear as second (vertical) coordinate). The EvaluationMonitor option can be helpful in situations like these. $\endgroup$
    – Michael E2
    Oct 5, 2016 at 20:03
  • $\begingroup$ I used to work with constraints, but that had it's own issues, see mathematica.stackexchange.com/questions/127554/… . Due to the suggestion in that question, I switched to defining constraints via the piecewise function. Probably what I need is a way to use the "NonlinearInteriorPoint" function as suggested in mathematica.stackexchange.com/questions/69622/… where, unfortunately, no syntax is provided to use the function. $\endgroup$
    – Felix
    Oct 6, 2016 at 0:57

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.