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Re: Unable to generate any initial points with NMaximize (or NMinimize)

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  • Subject: [mg131073] Re: Unable to generate any initial points with NMaximize (or NMinimize)
  • From: Dana DeLouis <dana01 at icloud.com>
  • Date: Sun, 9 Jun 2013 04:31:49 -0400 (EDT)
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Hello.  It appears you don't have a response, so I'll give it a try.

>       a > $MachineEpsilon

When you have a constraint such as this, you are saying that a solution of 4.440892*10^-16
is not really zero, and a valid solution.

2*$MachineEpsilon//N
4.440892*10^-16


For optimization problems, using ">" is usually a problem because of limits.  I believe one should use ">=" for constraints.

If 'a was found to be around 0.000001, the program has to retry with a number smaller than this, yet greater than MachineEpsilon.  The next try might be at 0.0000001, etc.  There's not really a number smaller than MachineEpsilon (at machine precision of course) so what is the software to do?

Try using ">="

equ=1/(0.` +(0.012710615354858255` ... etc   //FullSimplify;

const={a>=0,b>=0,fm>=0,c>=0,p>=0,
fm<=5,0.00009600189408524172` (5-fm)-40.451710009005595` b fm>=0};


{val,sol}=NMaximize[{equ,const},{a,b,fm,c,p},MaxIterations->1000]


However, I don't believe this problem has a solution as given.  :>~



= = = = = = = = = =

HTH  :>)

Dana DeLouis

Mac & Mathematica 9

= = = = = = = = = =







On Thursday, May 23, 2013 3:16:08 AM UTC-4, Meike wrote:

> I often get the error:

>

> NMaximize::incst: NMaximize was unable to generate any initial points satisfying the inequality constraints

> while there are clearly points satisfying the inequality constraints. For example:

> NMaximize[{1/(0.` + (0.012710615354858255` (0.07879657698200958` +

>           a) (0.000046296899009293725` +

>           0.003958158898356454` b) (233.02777267494722` +

>           102.02996575509754` fm))/(a (4.892449413727213`*^-6 -

>           9.784898827454427`*^-7 fm - 0.4123000838756304` b fm)) + (

>      0.10155110608580004` (0.0367973376747971` +

>         c) (0.5030193912642286` + 16.257272679476753` b +

>         0.0309411917473244` p))/b + (

>      219.22680202984347` (0.03970570642848887` +

>         0.013422101464134875` fm) (0.07972967880969935` +

>         0.14421246041749264` p))/(fm p)), a > $MachineEpsilon,

>   b > $MachineEpsilon, fm > $MachineEpsilon, c > $MachineEpsilon,

>   p > $MachineEpsilon,

>

>   0.00009600189408524172` (5 - fm) -

>

>     40.451710009005595` b fm > $MachineEpsilon, fm < 5.`}, {a, b, fm,

>

>   c, p}, MaxIterations -> 1000]

>

>

>

> NMaximize::incst: NMaximize was unable to generate any initial points satisfying the inequality constraints {-0.000480009+0.0000960019 fm+40.4517 b fm<0}. The initial region specified may not contain any feasible points. Changing the initial region or specifying explicit initial points may provide a better solution. >>

>

>

>

> Clearly there are initial points, for example:

>

>

>

> 0.00009600189408524172` (5 - fm) -

>

>    40.451710009005595` b fm > $MachineEpsilon /. {b -> 0.0007,

>

>   fm -> 0.00003}

>

>

>

> True

>

>

>

> Also, if I make a more simple example with the same constraint I do not get the same error. I know I could give initial values myself, but since I'm automatically generating many of the optimizations, I would prefer not to. And I would like to understand why I keep getting this error and if there is any way to solve it.





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