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# RE: st: Optimize

 From Mohamud Hussein To "statalist@hsphsun2.harvard.edu" Subject RE: st: Optimize Date Tue, 24 Jul 2012 13:16:25 +0100

```Many thanks Austin - your adjusted code works!

Now, I would like to set two constraints based on variables in my data:

m= a probability for a test protocol to detect presence of a pathogen in a sample. This variable ranges 0-100%; and

n= a numerical code (1, 2 and 3) for three alternative test protocols.

Question: how I can include these constraints into your mata code, and is it possible to use both constraints at the same time?

Thanks again,
Mohamud

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: 23 July 2012 19:53
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Optimize

Matthew Baker <matthew.baker@hunter.cuny.edu>:
That code minimizes the first derivative, according to the OP. I think
the OP wants to find the minimum of the cubic given, which means
setting the quadratic to zero in the case of an interior solution
(i.e. just use the quadratic formula, not Mata). But there are no
interior solutions for a cubic with positive coefs, so the OP needs to
substitute in any constraints holding with equality.  Or perhaps I am
misunderstanding the desideratum here.

On Mon, Jul 23, 2012 at 2:30 PM, Matthew Baker
<matthew.baker@hunter.cuny.edu> wrote:
> Mohamud --
>
> I think there are a few things wrong with the code that you presented
> below. For one, I think you want the arguments of your void function
> to be (todo,x,crit,g,H) - otherwise, as written, you are not returning
> anything to the evaluator! Moreover, your objective function omits a
> few operators so I think it should be (3*x^2+2*x+1)^2.
>
> Given those few changes, a simplified version of your code that might
> get closer to what you want is something like:
>
> /* begin example */
> clear all
> mata:
> void q(todo,x,crit,g,H)
> {
>  crit=(3*x^2+2*x+1)^2
> }
> real matrix grid(n1,n2)
> {
>  real matrix sol
>  real scalar i,p
>  sol=J(0,2,0)
>  for (i=n1; i<=n2; i++) {
>  init=i
>  S=optimize_init()
>  optimize_init_evaluator(S, &q())
>  optimize_init_which(S,"min")
>  optimize_init_evaluatortype(S,"d0")
>  optimize_init_params(S,init)
>  p=round(optimize(S),10e-8)
>  sol=sol \ (i,p)
>  }
>  return(sol)
>  }
> grid(-10,10)
> end
> /* end example */
>
> Hope that helps!
>
> Matt Baker
>
>
> On Mon, Jul 23, 2012 at 11:45 AM, Mohamud Hussein
> <Mohamud.Hussein@fera.gsi.gov.uk> wrote:
>> Thanks Austin.
>>
>> I used code below as suggested but had no luck yet. I am sure it has something to do with my complete lack of knowledge in mata language.
>>
>> I attach my data. I would be grateful if you can check for me where I am getting it wrong.
>>
>> Many thanks,
>> Mohamud
>>
>> ==
>>
>> void q(todo,x,y,g,H)
>> {
>>  crit=(3x^2+2x+1)^2
>> }
>> sol=J(1,0,0)
>> void grid(n1,n2)
>> {
>>  external sol, p
>>  for (i=n1; i<=n2; i++) {
>>   init=i
>>  S=optimize_init()
>>  optimize_init_evaluator(S, &q())
>>  optimize_init_which(S,"min")
>>  optimize_init_evaluatortype(S,"d0")
>>  optimize_init_params(S,init)
>>  p=round(optimize(S),10e-4)
>>  if (!anyof(sol, p)) {
>>   sol=(sol,p)
>>   }
>>  }
>>  sol
>> }
>> grid(-10,10)
>>
>> ==
>>
>>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
>> Sent: 23 July 2012 15:26
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: Optimize
>>
>> Mohamud Hussein <Mohamud.Hussein@fera.gsi.gov.uk>:
>> Looks like you are trying to maximize the unbounded quadratic rather
>> than find its zeros.  Use a root finder instead e.g.
>> http://www.stata.com/statalist/archive/2007-12/msg00551.html
>> http://www.stata.com/statalist/archive/2009-01/msg01140.html
>> but note first that the particular example you gave has no zeros (so
>> no interior solution).
>>
>> On Sun, Jul 22, 2012 at 9:59 AM, Mohamud Hussein
>> <Mohamud.Hussein@fera.gsi.gov.uk> wrote:
>>> Hi there,
>>>
>>> I am trying to run a model for a marginal cost curve equation based on the traditional cubic total cost curve function (i.e. y= x^3+X^2+X+c) using Stata's optimize() command. The goal is to estimate the value of x which minimises y subject to a number of constraints.
>>>
>>> When I tried to specify the marginal cost curve function in mata directly as y=3x^2+2x+1 (i.e. first derivative of the total cost equation) I got the following message:
>>>
>>> Iteration 0:   f(p) =          1  (not concave)
>>> Iteration 1:   f(p) =  7.911e+71  (not concave)
>>> Iteration 2:   f(p) =  1.95e+169  (not concave)
>>> Iteration 3:   f(p) =  8.32e+250  (not concave)
>>> Iteration 4:   f(p) =  1.62e+288  (not concave)
>>> Iteration 5:   f(p) =  2.34e+306
>>> Hessian is not negative semidefinite
>>>
>>> I have never used Stata's mata programming language before and am not quite sure of what do here? Grateful if someone can help me on this.
>>>
>>> Thanks,
>>> Mohamud
>>
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