Quadratic programming

Hi,

Sorry, for my rushed responses, last night.
(Shouldn't post when I'm about to log out).

I haven't used the quadprog package for nearly a decade.
And I was hoping that an expert using optimization in finance in
economics would reply.

Some comments:
(1) I don't know why you think bvec should be a matrix. The
documentation clearly says it should be a vector (implying not a
matrix).
The only arguments that should be matrices are Dmat and Amat.
(2) I'm having some difficulty following your quadratic program, even
after rendering it.
Perhaps you could rewrite your expressions, in a form that is
consistent with the input to solve.QP. That's a math problem, not an R
programming problem, as such.
(3) If that fails, then you'll need to produce a minimal reproducible example.
I strongly recommend that the R code matches the quadratic program, as
closely as possible.


On Mon, Sep 21, 2020 at 9:28 PM Maija Sirkj?rvi
<maija.sirkjarvi at gmail.com> wrote:

Hi!

I was wondering if someone could help me out. I'm minimizing a following
function:

\begin{equation}
$$\sum_{j=1}^{J}(m_{j} -\hat{m_{j}})^2,$$
\text{subject to}
$$m_{j-1}\leq m_{j}-\delta_{1}$$
$$\frac{1}{Q_{j-1}-Q_{j-2}} (m_{j-2}-m_{j-1}) \leq \frac{1}{Q_{j}-Q_{j-1}}
(m_{j-1}-m_{j})-\delta_{2} $$
\end{equation}

I have tried quadratic programming, but something is off. Does anyone have
an idea how to approach this?

Thanks in advance!

Q <- rep(0,J)
for(j in 1:(length(Price))){
  Q[j] <- exp((-0.1) * (Beta *Price[j]^(Eta + 1) - 1) / (1 + Eta))
}

Dmat <- matrix(0,nrow= J, ncol=J)
diag(Dmat) <- 1
dvec <- -hs
Aeq <- 0
beq <- 0
Amat <- matrix(0,J,2*J-3)
bvec <- matrix(0,2*J-3,1)

for(j in 2:nrow(Amat)){
  Amat[j-1,j-1] = -1
  Amat[j,j-1] = 1
}
for(j in 3:nrow(Amat)){
  Amat[j,J+j-3] = -1/(Q[j]-Q[j-1])
  Amat[j-1,J+j-3] = 1/(Q[j]-Q[j-1])
  Amat[j-2,J+j-3] = -1/(Q[j-1]-Q[j-2])
}
for(j in 2:ncol(bvec)) {
  bvec[j-1] = Delta1
}
for(j in 3:ncol(bvec)) {
  bvec[J-1+j-2] = Delta2
}
solution <- solve.QP(Dmat,dvec,Amat,bvec=bvec)

        [[alternative HTML version deleted]]