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Saad
Posts:
23
Registered:
11/26/12


Re: fminunc + transformation
Posted:
Apr 11, 2013 2:27 PM


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 interiorpoint or sqp algorithms, which respect bounds. > >> http://www.mathworks.com/help/optim/ug/writingconstraints.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 (interiorpoint 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/refiningthestartpoints.html#bsfjxr9 > http://www.mathworks.com/help/gads/isolatedglobalminimum.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','interiorpoint','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



