Im trying to solve the following problem in R, using the quadprog package:
min: vec %*% p + t(p) %*% mat %*% p
st: p >= 0
where
mat <- matrix(c(1162296,0,0,0,0,1,0,0,951.7089,0,1,0,-951.7089,0,0,1),4)
vec <- c(6341934541.1,175800.1,-356401.7,14398073047.1)
I've used
libary(quadprog)
solve.QP(2*mat,-vec, diag(4), integer(4))
but I keep getting the following error:
Error in solve.QP(2*mat, -vec, diag(4), integer(4)) :
matrix D in quadratic function is not positive definite!
However, cleary
> eigen(mat)$values > 0
[1] TRUE TRUE TRUE TRUE
What am I doing wrong? How come this error keeps showing up?
Your matrix mat is not symmetric. The quadprog package is designed to solve quadratic programs, which by definition, require a symmetric matrix in the highest order term. See here, for example.
To solve this problem as written, you will need to use a general constrained optimization algorithm. For example, you can try constrOptim as so:
# system matrices
mat <- matrix(c(1162296,0,0,0,0,1,0,0,951.7089,0,1,0,-951.7089,0,0,1),4)
vec <- c(6341934541.1,175800.1,-356401.7,14398073047.1)
# an initial value
p0 <- c(1,1,1,1)
# the objective function
objective <- function(p) {
vec %*% p + t(p) %*% mat %*% p
}
# solve -- warning! without additional work you won't know if this is a global minimum solution.
solution <- constrOptim(p0, objective, NULL, diag(4), c(0,0,0,0))