How to include matrix multiplication in constraint? - r

Question

I am trying to make run this model. I am trying to maximize:x[4]
w.r.t Mv = c(0,0,0,0)
lb < v < ub
But I have 2 problems, first matrix multiplication.
library(ompr)
lb <- c(-200, 0, -200, -200)
ub <- c(1000, 1000, 1000, 1000)
M <- matrix(rbind(
c(-1, 0, -1, 0), # A
c(-1, 0, 0, -2), # B
c(1, -2, 0, 0), # C
c(1, 0, 0, 2), # D
c(0, 2, -1, 0), # E
c(0, 0, 1, -1) # F
), nrow = 6)
n <- 4
rhs <- rep(0, n)
model <- MIPModel() %>%
add_variable(x[i], i = 1:n, type = "continuous") %>%
set_objective(x[4]) %>%
add_constraint(M[i, ] %*% x == rhs[i], i = 1:n)
I got the following error.
Error in M[i, ] %*% x : requires numeric/complex matrix/vector
arguments
Second, I am trying to set the bounds in a vectorized way, but I don't know how to do that. I tried the following:
set_bounds(x[i], ub = ub[i], lb = lb[i], i = 1:n)
This gives:
object 'i' not found
Any help would be very useful!

Answer 1

Works like this, but the solution is (0, 0, 0, 0):
library(ompr)
library(ompr.roi)
library(ROI.plugin.glpk)
library(magrittr)
lb <- c(-200, 0, -200, -200)
ub <- c(1000, 1000, 1000, 1000)
M <- matrix(rbind(
c(-1, 0, -1, 0), # A
c(-1, 0, 0, -2), # B
c(1, -2, 0, 0), # C
c(1, 0, 0, 2), # D
c(0, 2, -1, 0), # E
c(0, 0, 1, -1) # F
), nrow = 6)
n <- 4
rhs <- rep(0, n)
model <- MIPModel() %>%
add_variable(x[i], i = 1:n, type = "continuous") %>%
set_objective(x[4], "max") %>%
add_constraint(sum_over(M[i, j] * x[j], j = 1:4) == rhs[i], i = 1:n) %>%
add_constraint(x[i] <= ub[i], i = 1:n) %>%
add_constraint(x[i] >= lb[i], i = 1:n) %>%
solve_model(with_ROI(solver = "glpk"))
get_solution(model, x[i])