On 15 October 2013 16:55, MM <[email protected]> wrote: > On 15 October 2013 16:43, Steven G. Johnson <[email protected]> wrote: > >> >> On Oct 15, 2013, at 9:40 AM, MM <[email protected]> wrote: >> > 1. Can nlopt be used for such a problem? >> >> Yes, it sounds like a standard nonlinear-constrained optimization problem. >> >> Also, the constraints here are _not_ on the input variables (the vector X), but on the objective functions themselves. Is this handled?
> > 2. Can the problem be simplified to dealing just with f2 and f3? >> >> I don't see how you can possibly remove your objective f1 from the >> problem. >> > > Just to make sure I expressed myself correctly here: f1 is simply = f2/f3. > In order of priority, I want to maximize f1, then maximize f2 with > f2>=min2, and minimize f3<=min3, if there is such a solution(s) > > I could formulate the problem as: maximize f2 and minimize f3 (this may > be a Pareto frontier), and then choose the point on this frontier that > gives the max f2/f3 > > Thanks, > > > Ultimately, I am not looking for the absolute max of f1(X) in the >> feasible region, >> > I am looking for the "ball" or "hypercube" of length E in each >> dimension, inside the feasible region, such that the average of f1(X) over >> that hypercube is maximum. >> >> This sounds like it is just a change of objective. Instead of your >> objective being f1, it would be the mean of f1 over a ball of diameter E >> centered at X. >> >> > Just to clarify >
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