[R] Quadprog help

[Moshe Olshansky]

Hi Sergio,

Having singular Dmat is certainly a problem.
I can see two possibilities:
1) try to eliminate X1,...,X9, so that you are left with P1,...,P6 only.
2) if you can not do this, add eps*X1^+...+eps*X9^2 to your matrix Dmat so that it is positive definite (eps is a small positive number). You can then try to make eps smaller and smaller (but still not too small in order not to get into numerical problems) and check whether your solution converges.

--- On Fri, 19/2/10, Araujo-Enciso, Sergio Rene <Sergio-Rene.Araujo-Enciso at agr.uni-goettingen.de> wrote:

> From: Araujo-Enciso, Sergio Rene <Sergio-Rene.Araujo-Enciso at agr.uni-goettingen.de>
> Subject: [R] Quadprog help
> To: r-help at r-project.org
> Received: Friday, 19 February, 2010, 7:40 PM
> I am having some problems using
> Quadprog in R. I want to minimize the
> objective function :
> 
>  
> 
> 200*P1-1/2*10*P1^2+100*P2-1/2*5*P2^2+160*P3-1/2*8*P3^2+50*P4-1/2*10*P4^2+50*P
> 5-1/2*20*P5^2+50*P6-1/2*10*P6^2, 
> 
>  
> 
> Subject to a set of constrains including not only the
> variables P1, P2, P3,
> P4, P5, P6, but also the variables X1,
> X2,X3,X4,X5,X6,X7,X8,X9.
> 
>  
> 
>  As the set of variables X's are not affecting the
> objective function, I
> assume that I have to enter them as zero's in the vector
> "dvec" and the
> matrix "Dmat". 
> 
>  
> 
> My program states as: 
> 
>  
> 
> mat<-matrix(0,15,15)
> 
> diag(Dmat)<-c(10,5,8,10,20,10,0,0,0,0,0,0,0,0,0)
> 
> dvec<- c(-200,-100,-160,-50,-50,-50,0,0,0,0,0,0,0,0,0)
> 
> Amat<-
> matrix(c(-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,
> 
>              
>    0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,
> 
>              
>    0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,
> 
>              
>    0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
> 
>              
>    0,-1,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
> 
>              
>    1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,
> 
>              
>    0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,
> 
>              
>    -10,0,0,0,0,0,-1,0,0,-1,0,0,-1,0,0,0,-5,0,
> 
>              
>    0,0,0,0,-1,0,0,-1,0,0,-1,0,0,0,-8,0,0,0,0,
> 
>              
>    0,-1,0,0,-1,0,0,-1,0,0,0,-10,0,0,1,1,1,0,0,
> 
>              
>    0,0,0,0,0,0,0,0,-20,0,0,0,0,1,1,1,0,0,0,0,0,
> 
>              
>    0,0,0,-10,0,0,0,0,0,0,1,1,1),15,15)
> 
> bvec
> <-c(0,-2,-2,-2,0,-1,-2,-1,0,-200,-100,-160,-50,-50,-50)
> 
> solve.QP(Dmat,dvec,Amat,bvec=bvec)
> 
>  
> 
> Nonetheless I get the message: "Error en solve.QP(Dmat,
> dvec, Amat, bvec =
> bvec) : matrix D in quadratic function is not positive
> definite!".
> 
>  
> 
> I think it has to do with the fact that in the Dmat matrix
> I end up with
> several columns with zeros. Do anyone have an idea of how
> to solve such a
> problem? 
> 
>  
> 
> Bests, 
> 
>  
> 
> Sergio René
> 
> 
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> 
> 
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