Constraint Problem

[benubah]

Hi,
I am porting an example of CVXPY using CVXR in R found here: https://groups.google.com/forum/#!topic/cvxpy/5hBSB9KVbuI

The Python Code:

import numpy as np
np.random.seed(1)
n = 8
m = 2
T = 50
alpha = 0.2
beta = 5
A = np.eye(n) + alpha*np.random.randn(n,n)
B = np.random.randn(n,m)
x_0 = beta*np.random.randn(n,1)

from cvxpy import *
x = Variable(n, T+1)
u = Variable(m, T)

states = []
for t in range(T):
    cost = sum_squares(x[:,t+1]) + sum_squares(u[:,t])
    constr = [x[:,t+1] == A*x[:,t] + B*u[:,t],
              norm(u[:,t], 'inf') <= 1]
    states.append( Problem(Minimize(cost), constr) )
# sums problem objectives and concatenates constraints.
prob = sum(states)
prob.constraints += [x[:,T] == 0, x[:,0] == x_0]
prob.solve()

This the R code:

n = 8
m = 2
T1 = 50
alpha = 0.2
beta = 5
A = pracma::eye(n) + alpha*pracma::randn(n,n)
B = pracma::randn(n,m)
x_0 = beta*pracma::randn(n,1)
x = Variable(n, T1+1)
u = Variable(m, T1)

states = c()
for (t in 1:T1) {
  cost = sum_squares(x[,t+1]) + sum_squares(u[,t])
constr = list(x[, t+1] == A*x[, t] + B*u[, t], pracma::Norm(u[,t], Inf) <= 1)
states = append(states, Problem(Minimize(cost), constr) )
}
prob = sum(states)
prob.constraints += [x[ ,T1] == 0, x[ ,0] == x_0]
prob.solve()

I am getting the following error:

Error in sum_shapes(lapply(object@args, function(arg) { :
Incompatible dimensions

I am suspecting it is from the following statement in the for loop because taking that line out shows a different case:

constr = list(x[, t+1] == Ax[, t] + Bu[, t], pracma::Norm(u[,t], Inf) <= 1)

Please could you look into this and suggest what could be possibly the cause for this error.

Thank you.

[anqif]

You need to use R's semantics for matrix multiplication, i.e. A %% x[,t] + B %% u[,t]. The operator * refers to elementwise multiplication, which requires the operands to have the same dimensions, hence the error.

[benubah]

Thank you for your quick response.
I had tried that out before now and it usually shows another error:
Error: is.numeric(x) || is.complex(x) is not TRUE

To be sure where the problem lies, I had to comment out the remaining part of the program after the for loop.

Thanks

[anqif]

CVXR does not support the combination of pracma library functions with CVXR objects such as your variables, x and u. You should use R's built-in eye, rnorm in place of randn, and CVXR's norm_inf.

[benubah]

Hi,

thank you!
Just using norm_inf() solves the error.
However, another error (Error in min(constant) : invalid 'type' (list) of argument) is shown by the following line:
prob = sum_entries(states)

The updated R code is:

#np.random.seed(1)
set.seed(1)
n = 8
m = 2
T1 = 50
alpha = 0.2
beta = 5
A = diag(n) + alpha*replicate(n, rnorm(n))
B = replicate(m, rnorm(n))
x_0 = beta*replicate(1, rnorm(n))
x = Variable(n, T1+1)
u = Variable(m, T1)
states = c()
for (t in 1:T1) {
  cost = sum_squares(x[,t+1]) + sum_squares(u[,t])
constr = list(x[, t+1] == A%*%x[, t] + B%*%u[, t],
         norm_inf(u[,t]) <= 1)
states = c(states, Problem(Minimize(cost), constr) )
}
# sums problem objectives and concatenates constraints.
prob = CVXR::sum_entries(states)
prob.constraints += list(x[ ,T1] == 0, x[ ,0] == x_0)
prob.solve()

How could the second-to-last line (concatenating constraints) be represented using CVXR:
prob.constraints += list(x[ ,T1] == 0, x[ ,0] == x_0)

Thank you very much for your kind assistance.

[anqif]

You cannot just copy the Python code, you need to understand what it is doing and rewrite it using R's syntax. For instance, you want to sum the problems, which are contained in the list states, so you must use R's Reduce function, i.e. Reduce("+", states). The next line concatenates a new constraint to prob's list of constraints, which is done using c().

I'm closing this thread since none of these are bugs with CVXR. You should work through the examples at http://cvxr.rbind.io/.