CVXGEN: Code Generation for Convex Optimization

Indexed parameters and variables

Many optimization problems contain a sequence of variables or parameters, indexed by time or some other offset. For example, in a model predictive control (MPC) problem, the state variables are typically $x^{(0)}, ldots, x^{(T)} in mathbf{R}^n$ . Rather than declare all T+1 variables individually, CVXGEN provides special syntax to work with indexed variables. Here are some examples:

parameters
  A[i] (m,n) nonnegative, i=1..3
end

variables
  x[t] (n), t=0..T
  z[tau], tau=-L..L
end

In CVXGEN's mbox{LaTeX} output, these will be indexed with a superscript, bracketed index, such as $z^{(-2)}$ .

Indexed symbols can be used in sum functions like sum[t=0..T](x[t]), or in indexed constraints.

Notes

If you're looking to instead index into a single vector, see this page.
You can use any variable name for the index, but be sure the two instances match.
You can use symbolic dimensions and simple arithmetic in the limits.
Indices can be zero or positive. Negative indices are not supported.