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Topic: fsolve trust-region radius question
Replies: 2   Last Post: Apr 9, 2013 10:26 AM

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Alan Weiss

Posts: 1,261
Registered: 11/27/08
Re: fsolve trust-region radius question
Posted: Apr 9, 2013 10:21 AM
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On 4/9/2013 8:11 AM, Anna wrote:
> Hello,
>
>
> I have a system of non-linear equations and i am trying to solve if
> with fsolve.
>
> I get a solution as function value is approaching 0, which is correct.
> But trust-region radius value increases towards the end. Does it mean
> that solution is not valid?
>
>
> My output:
>
>
> Iteration Func-count f(x) step optimality radius
> 0 4 1.81987e+17 1.79e+17 1
> 1 8 1.20317e+16 1 2.34e+16 1
> 2 12 7.51981e+14 2.5 2.92e+15 2.5
> 3 16 4.69988e+13 6.25 3.65e+14 6.25
> 4 20 2.93743e+12 15.625 4.57e+13 15.6
> 5 24 1.83589e+11 39.0625 5.71e+12 39.1
> 6 28 1.14744e+10 96.1258 7.14e+11 97.7
> 7 32 7.17156e+08 79.7071 8.92e+10 240
> 8 36 4.48229e+07 39.8535 1.12e+10 240
> 9 40 2.80148e+06 19.9267 1.39e+09 240
> 10 44 175094 9.96322 1.74e+08 240
> 11 48 10942.3 4.98133 2.18e+07 240
> 12 52 683.465 2.49012 2.72e+06 240
> 13 56 42.5875 1.24396 3.41e+05 240
> 14 60 2.62715 0.619798 4.26e+04 240
> 15 64 0.155563 0.305586 5.32e+03 240
> 16 68 0.00783099 0.144585 660 240
> 17 72 0.000214572 0.0586426 73.3 240
> 18 76 8.39263e-07 0.0144368 4.03 240
> 19 80 5.05294e-11 0.00102595 0.031 240
> 20 84 4.49694e-16 8.03849e-06 9.24e-05 240
> 21 88 3.90081e-21 2.39824e-08 2.72e-07 240
>
> Equation solved.
>
> fsolve completed because the vector of function values is near zero
> as measured by the default value of the function tolerance, and
> the problem appears regular as measured by the gradient.
>
>
> y =
>
> 2.3911 -0.3713 0.0006
>
>
> fval =
>
> 1.0e-10 *
>
> -0.0000
> 0.0000
> 0.6246
>
>
> exitflag =
>
> 1
>
>
> Thanks in advance!


A large value of the trust-region radius means the solver believes that
its internal model of the function is valid for a large region. Worry
about a small trust-region radius, and be happy with a large one.

Alan Weiss
MATLAB mathematical toolbox documentation



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