Re: Re: Solving nonlinear inequality constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg91370] Re: [mg91243] Re: [mg91209] Solving nonlinear inequality constraints
• From: "Stuart Nettleton" <Stuart.Nettleton at uts.edu.au>
• Date: Tue, 19 Aug 2008 07:13:10 -0400 (EDT)
• Organization: University of Technology, Sydney
• References: <200808091147.HAA18525@smc.vnet.net>

```On Mon, 18 Aug 2008 03:26:22 +1000, <danl at wolfram.com> wrote:
> (1) Get rid of all the Hold usage. If you need it, you are doing
> something
> wrong.
>
> (2) If you spend a bit of time debugging this, say, computing various
> functions for various small values of t (e.g. inv[2]), you will quickly
> learn that you have not defined \[Mu][t_]. This means there will be no
> end
> of symbolic computation in trying to resolve various inequalities, etc.
>
> (3) There could be other issues. For one, you might have complex values
> which will cause inequalities to be unevaluated. This, too, might be
> determined by computing various values (after resolving issue (2) above).
>
> Daniel Lichtblau
> Wolfram Research
>
>
Hi Daniel, Thanks for your response. I have experiemented with your
suggestions but question whether your points can be implemented because of
the following issues:
(1) Hold usage cannot be removed on constraints because they immediately
start to evaluate for true/false eg. 0.02*k[periods] <= inv[periods],
which is not wanted because they need to remain symbolic to be combined
with the objective function (and because they burst the Recursion limit).
(2) \[Mu][t_] is deliberately not defined or else the the {x,y,...} in
NMinimize[{f,cons},{x,y,...}] are immediately evaluated. As with the
constraints, the {x,y,...} need to remain symbolic to be of use in
NMinimize. Instead of a using the function that you suggested, I have left
the \[Mu][t] to be provided by NMinimize. Given (1) and (2), how can your
suggestion can be implemented?
(3) Complex values do not arise with any of the cases I can evaluate but
it is agreed that this would need to be watched. Interestingly, using
NMinimize, 7 periods takes 35 minutes and 8 periods takes 77 minutes. The
memory usage is 2.3Gb and 11.3Gb respectively. Using _NumericQ in each of
the function definitions actually slows down execution by about 1 minute.
Stuart

--
Stuart Nettleton
Senior Lecturer, Faculty of Engineering

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