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Topic: fminunc + transformation
Replies: 5   Last Post: Apr 12, 2013 1:37 PM

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Alan Weiss

Posts: 1,259
Registered: 11/27/08
Re: fminunc + transformation
Posted: Apr 12, 2013 1:37 PM
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On 4/11/2013 2:27 PM, Saad wrote:
> Alan_Weiss <aweiss@mathworks.com> wrote in message
> <kjjqng$i08$1@newscl01ah.mathworks.com>...

>> On 4/4/2013 3:47 AM, Saad wrote:
>> >
>> >
>> > Alan_Weiss <aweiss@mathworks.com> wrote in message >

>> <kjhqkj$ioi$1@newscl01ah.mathworks.com>...
>> >> On 3/30/2013 5:26 PM, Saad wrote:
>> >> > Dear all,
>> >> >
>> >> > I am replicating a paper who recommends using fminunc to do a >

>> >> "constrained" optimization through a transformation. I have tried
>> to >> > use directly fmincon (with different algorithms) but the
>> function > >> doesnt optimize, thats the reason I would like to
>> follow the paper > >> advice and use a transformation as follows:

>> >> >
>> >> > C_bar=lamda*(exp(C)/1+ exp(C)) where lamda is a constant, C is

>> the >> > unconstrained variable and C_bar is the constrained
>> variable. I >> would > really appreciate if you could show me how I
>> could use the > >> transformation in matlab. Do I have to create a
>> seperate function? >> How > can I link it to the optimizer please?

>> >> >
>> >> > Here is my code
>> >> >
>> >> > C=[1; 1; 1 ; 1; 1; 1; 1; 1; 1];

>> >> > >>
>> options=optimset('Diagnostics','on','Display','iter','TolX',0.001,'TolFun',0.001,'LargeScale','off','HessUpdate','bfgs');
>> >> >
>> >> > [beta,fval,exitflag,output,grad,hessian] =fminunc(@mll,C,options)
>> >> >
>> >> > Thanks a lot for your help
>> >> >
>> >> > Best Regards
>> >> >
>> >> > S

>> >>
>> >> It looks to me as if C_bar is a multidimensional variable

>> constrained >> to be between 0 and 1. Is that right?
>> >>
>> >> You can certainly include this transformation in a MATLAB statement:
>> >>
>> >> C_bar = lamda.*(exp(C)./(1+exp(C));
>> >>
>> >> The ./ and .* statements mean componentwise division and

>> multiplication.
>> >>
>> >> However, I think you could avoid this complicated and (it seems to
>> >> me) fragile transformation by simply setting bounds on fmincon and
>> >> using the interior-point or sqp algorithms, which respect bounds.
>> >>

>> http://www.mathworks.com/help/optim/ug/writing-constraints.html#br9p_ry
>> >>
>> >> Good luck,
>> >>
>> >> Alan Weiss
>> >> MATLAB mathematical toolbox documentation

>> >
>> > Hi Alan
>> >
>> > Thank you for your reply. I did try fmincon with different >

>> algorithms (interior-point and sqp algorithms) but could not locate
>> > the minimum. I also tightened the tolerance but still could not >
>> minimize (for info i am working on a kalman filtering problem). I >
>> think the issue is that I am not able to find a good initial guess. >
>> Any thoughts on how to handle that? Thanks a lot

>> >
>> > Best
>> >
>> > S

>>
>> Well, assuming that you have upper and lower bounds on all
>> components, why not try a lot of random initial points?
>>
>> x0 = lb + rand(size(lb)).*(ub - lb);
>>
>> There are more suggestions here (written for Global Optimization
>> Toolbox, but you can use the suggestions anyway):
>> http://www.mathworks.com/help/gads/refining-the-start-points.html#bsfjxr9
>>
>> http://www.mathworks.com/help/gads/isolated-global-minimum.html
>>
>> Alan Weiss
>> MATLAB mathematical toolbox documentation

>
> Dear Alan
>
> Hope you are well. I tried your suggestions and used Global
> Optimization Toolbox and my new problem is defined as follows:
> %%%%%%%
> opts = optimset('Algorithm','interior-point','Hessian','lbfgs');
> problem = createOptimProblem('fmincon','x0',[2; 2; 2 ; 2; 3; 3; 3; 3;
> 3],'objective',@(beta)mll(beta,y,R,xx),...
> 'lb',[0;0; 0; 0; 0; 0; 0; 0; 0],'ub',[10; 10; 10; 10; 10; 10; 10;
> 10; 10], 'options',opts);
> gs = GlobalSearch;
> rng(14,'twister') % for reproducibility
> gs.NumTrialPoints = 1000;%1e5;
> gs.MaxTime = 300;
> [xg fvalg] = run(gs,problem)
>
> %%%%%
>
> I was just wondering how can I retrieve the hessian matrix once the
> optimization is finished? Thanks a lot
> Regards
>
> S


You cannot retrieve the Hessian automatically. It wouldn't do you much
good, even if you did retrieve it; see
http://www.mathworks.com/help/optim/ug/hessian.html#bsapedt

If you are at a local minimum that is not at a constraint boundary, you
can run the fminunc solver from the solution point and get the Hessian
that way. But if a constraint is active, I am not sure what you can do,
because even if you re-ran fmincon starting from that point, the
returned Hessian is unreliable.

Alan Weiss
MATLAB mathematical toolbox documentation



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