R help - Nov 2005 - Constraints in Quadprog

I'm having difficulty figuring out how to implement the
following set of constraints in Quadprog:

1). x1+x2+x3+x4=a1
2). x1+x2+x5+x6=a2
3). x1+x3+x5+x7=a3
4). x1+x2=b1
5). x1+x3=b2
6). x1+x5=b3

for the problem: MIN (x1-c1)2+(x2-c2)2+...+(x8-c8)2.

As far a I understand, "solve.QP(Dmat, dvec, Amat, bvec, meq=0,
factorized=FALSE)" reads contraints using an element-by-element
multiplication, i.e. Amat'*x, not using the matrix-product, i.e. 
Amat'%*%x, required for the sums on the left-hand-side of 1-6).

I would very much appreciate a suggestion on this problem.

Thank you,
Serguei Kaniovski

If I understand correctly, you are asking how solve.QP interprets the 
arguments.  I clarified this by constructing a problem I could work 
manually but that was sophisticated enough to seemingly answer your 
question:  minimize (x1^2+x2^2) subject to (x1+x2)=1.  I computed 
manually that the answer should be x1=x2=0.5.  (I used Lagrange 
multipliers, because that's the first thing that entered my head. 
However, I also could have substituted (1-x1) for x2 or used the 
"solver" in MS Excel.)

	  After reading the documentation and trying something that gave an 
error message, I got the following:

 > (QP1 <- solve.QP(Dmat=diag(2), dvec=rep(0,2),
+   Amat=matrix(rep(1,2), c(2,1)), bvec=1, meq=1))
$solution
[1] 0.5 0.5

$value
[1] 0.25

$unconstrainted.solution
[1] 0 0

$iterations
[1] 2 0

$iact
[1] 1

	  If this does not answer your question, have you studied the example 
with "?solve.QP"?  If this is still not adequate, PLEASE do read the 
posting guide! http://www.R-project.org/posting-guide.html and submit 
another post;  I believe that people who follow that guide generally get 
more useful replies quicker.

	  hope this helps.
	  spencer graves

Serguei Kaniovski wrote:
> I'm having difficulty figuring out how to implement the
> following set of constraints in Quadprog:
> 
> 1). x1+x2+x3+x4=a1
> 2). x1+x2+x5+x6=a2
> 3). x1+x3+x5+x7=a3
> 4). x1+x2=b1
> 5). x1+x3=b2
> 6). x1+x5=b3
> 
> for the problem: MIN (x1-c1)2+(x2-c2)2+...+(x8-c8)2.
> 
> As far a I understand, "solve.QP(Dmat, dvec, Amat, bvec, meq=0,
> factorized=FALSE)" reads contraints using an element-by-element
> multiplication, i.e. Amat'*x, not using the matrix-product, i.e. 
> Amat'%*%x, required for the sums on the left-hand-side of 1-6).
> 
> I would very much appreciate a suggestion on this problem.
> 
> Thank you,
> Serguei Kaniovski
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
-- 
Spencer Graves, PhD
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