[R] The smallest enclosing ball problem

[Hans W.Borchers]

Berend Hasselman <bhh <at> xs4all.nl> writes:
> 

It seems you are absolutely right. I always assumed a quadratic programming 
solver will -- as all linear programming solvers do -- automatically require 
the variables to be positive.

I checked it for some more examples in 10 and even 100 dimensions, and the 
results now agree. Still, it's a bit disappointing that 'quadprog' will not 
solve problems with 10 points in R^3, because the corresponding matrices are 
not positive definite.

Thanks
Hans Werner

> 
> After  having a closer look at this problem, I believe you did not include 
> the constraint x_i >= 0 in the call to solve.QP.
> So with this modification of your code
> 
> A <- matrix(rep(1,3),nrow=4,ncol=3,byrow=TRUE)
> A[2:4,] <- diag(3)   
> b <- c(1,0,0,0)
> 
> sol3 <- solve.QP(D, d, t(A), b, meq = 1) # first row of A is an equality
> sol3
> p0 <- c(C %*% sol3$solution)
> r0 <- sqrt(-sol3$value)
> p0
> r0
> sqrt(colSums((C - p0)^2))
> 
> one gets the correct answer.
> BTW LowRankQP seems to postulate x_i >=0 if I read its manual correctly.
> 
> Berend