The smallest enclosing ball problem
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