Re: Optimization
From: Peter Spellucci (spellucci_at_fb04373.mathematik.tu-darmstadt.de)
Date: 02/14/05
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Date: Mon, 14 Feb 2005 17:29:17 +0000 (UTC)
In article <cuqh6i$fg0$1@orkan.itea.ntnu.no>,
Olw <anders@kommtek.com_NOSPAM> writes:
>Peter Spellucci wrote:
>> In article <cuqbod$c7i$1@orkan.itea.ntnu.no>,
>> Olw <anders@kommtek.com_NOSPAM> writes:
>> >I'm using Matlab's fmincon to find the maximum of a function f(x).
>> >(Constrained optimization)
>> >
>> > From plotting the function a that we have a feasible maximum for
>> >x=450, f(450)=11.4, But as the function varies relativly slow, only
>> >about 0.2 from
>> >x=250-700 the algorithms won't find the maxima.
>> >Matlab seems to return f(x_max) when x_max is about 700.
>> >
>> >
>> >Is there a way to transform the problem so that the maximum can be
>> >found? If I plot the function versus x in dB the graph looks "better",
>> >i.e. it varies more rapid versus the dB axis.
>> >
>> >If this dB thing is the way to do this how do I change my equations and
>> >constraints to incorporate this?
>> >
>> >Thanks,
>> >
>> >Olw
>>
>> you might try to compute the Hessian matrix of the Lagrangian function of
>> the problem . A rule of thumb says that the primal scaling should be such
>> that its diagonal is approximately the unit matrix (for the convex case).
>> hence use x=D^{-1/2}z as the scaling with D this diagonal.
>> you can influence the behaviour of fmincon by strengthen the rather sloppy
>> tolerance criteria, TolX and TolFun.
>> hth
>> peter
>Thank you for valuable help.
>
>I will try first to adjust the sloppy criteria, as it is very easy to
>see when the optimization yields erronous results.
>
>I will also look into this scaling business. Do you have any reference
>on this?
>
>Olw
Zbl 0491.90083 Lasdon, L.S.; Beck, P.O.
Scaling nonlinear programs. (English)
Oper. Res. Lett. 1, 6-9 (1981). MSC 2000: *90C30 65K05 90C99
40. Zbl 0517.49022 Grandinetti, L.
Nonlinear scaling algorithms for unconstrained optimization. (English)
Control applications of nonlinear programming and optimization, Coll. Pap., 2nd IFAC Workshop, Oberpfaffenhofen/Ger. 1980, 148-156 (1980). MSC 2000: *49M15 49J10 65K05
also discussed in
Gill;Murray;Wright: Practical optimization (Acad. Press)
hth
Peter
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