[R] how to use solve.QP

[roger bos]

At the risk of ridicule for my deficient linear algebra skills, I ask
for help using the solve.QP function to do portfolio optimization.  I
am trying to following a textbook example and need help converting the
problem into the format required by solve.QP.  Below is my sample code
if anyone is willing to go through it.  This problem will not solve
because it is not set up properly.  I hope I included enough details
for someone to deciper it.  Or does anyone have a good example they
can send me?

Thanks so much for any hints and suggestions, Roger.



library(quadprog, lib.loc="C:\\Program Files\\R\\tools")
library(MASS, lib.loc="C:\\Program Files\\R\\tools")
n<-100
m<-200
rho<-0.7
sigma<-0.2
mu<-0.1
Cov <- matrix(rho*sigma*sigma, ncol=n, nrow=n)
diag(Cov) <- rep(sigma*sigma, n)
S <- 1+matrix(mvrnorm(m, rep(mu, n), Sigma=Cov), ncol=n)

#The problem is formulated as minimize t(b) Cov b
#subject to cLo <= A <= cUp
#and bLo=0 <= w <= 1=bUp

Cov <- var(S)
mu <- apply(S, 2, mean)
mu.target <- 0.1
#subject to cLo <= A <= cUp and bLo=0 <= b <= 1=bUp
A <- rbind(1,mu)
cLo <- c(1, mu.target)
cUp <- c(1, Inf)
bLo <- rep(0, n)
bUp <- rep(1, n)

#I convert [cLo <= A <= cUp] to Amat >= bvec and [bLo=0 <= w #<=1=bUp] to
Amat <- rbind(-1, 1, -mu, mu)
dim(bLo) <- c(n,1)
dim(bUp) <- c(n,1)
bvec <- rbind(-1, 1, mu.target, Inf, bLo, -bUp)
zMat <- matrix(rep(0,2*n*n),ncol=n, nrow=n*2)
zMat[,1] <- c(rep(1,n), rep(-1,n))
Amat <- t(rbind(Amat, zMat))

#So I set Dmat=Cov and set dvec=0
Dmat=Cov
dvec=rep(0, nrow(Amat))

#The first two rows of Amat should be equality constraints (so weights sum to 1)
meq <- 2
					
sol <- solve.QP(Dmat=Dmat, dvec=dvec, Amat=Amat, bvec=bvec, meq)
sol