I would like to solve a maximization problem which itself depends on a maximization. I came up with this code,

f[w_, p_] := -p^2 + p w  
g[w_] := w - pR[w]^2    (These functions are chosen to illustrate the problem, the real functions are more complicated and can only be solved numerically)

pR[w_] := NArgMax[{f[w, p], p > 0, w > 0}, p]
J[w_?NumericQ] := g[w]
NMaximize[{J[w], w > 0, f[w, pR[w]] > 0.5}, w, 
 Method -> "RandomSearch"]

If I would drop the condition f[w, pR[w]] > 0.5, the code works fine, but with this expression my code runs into problems with the constraints.

Any idea how to solve this?

Thanks in advance Paul



f[w_?NumericQ, p_?NumericQ] := -p^2 + p w

pR[w_?NumericQ] := Block[{p}, NArgMax[{f[w, p], p > 0}, p]]
J[w_?NumericQ] := w - pR[w]^2
NMaximize[{J[w], {w > 0 , f[w, pR[w]] > 0.5}}, w ,EvaluationMonitor :> Print[{w, J[w]}]
,Method->"NelderMeat", AccuracyGoal -> 3]
(*{1., {w -> 2.00012}}*)

It works with slow convergence in Mathematica v12...

  • $\begingroup$ Thx Ulrich, the code converged at 2.0007 for me. However, i got the following errors : 1) NArgMax::bcons: The following constraints are not valid: {p>0,w>0}. Constraints should be equalities, inequalities, or domain specifications involving the variables. $\endgroup$ – Paul Nov 12 '19 at 14:46
  • $\begingroup$ Try "NelderMeat" (see my edited answer). Mathematica v12(Windows 7) evaluates without error. $\endgroup$ – Ulrich Neumann Nov 12 '19 at 14:52
  • $\begingroup$ I try the new method, thx $\endgroup$ – Paul Nov 12 '19 at 14:54
  • $\begingroup$ Thx again, i am getting again closer. $\endgroup$ – Paul Nov 12 '19 at 17:35
  • $\begingroup$ it would be amazing if you could have a look on the next problem I stumbled in :-( mathematica.stackexchange.com/questions/209492/… $\endgroup$ – Paul Nov 12 '19 at 17:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.