I have the following convex optimization problem:

$$ \begin{align*} \min_{x} &f(x) \\ \text{subject to} \\ x_{k+1} &= x_k+\cdots\qquad k=0,1,2,\ldots,N-1 \end{align*} $$

I managed to solve the above problem using YALMIP, using its very fast optimizer parser. Unfortunately, while optimizer can give me the dual variables associated with my $N$ constraints, it gives them out of order - in other words, the second element in the array of duals that optimizer returns does not necessarily correspond to the dual of the constraint $x_2=x_1+\cdots$.

Question: how can I recover the duals of this optimization problem, either by direct calculation or by matching the out-of-order duals that I have with the constraints?

I think this is a mathematical question rather than a programming one. In the end, I'm just asking how I can compute the duals of an already-solved optimization problem.

  • $\begingroup$ You're better off asking that question on the YALMIP forum as this is very YALMIP specific. I don't see why the order would be changed for this problem, so please post an MVE on the YALMIP forum and I'll try to answer it there. $\endgroup$ May 11 '16 at 17:47
  • $\begingroup$ It's not straightforward, see comments and answer to this question: math.stackexchange.com/questions/1279435/… $\endgroup$
    – user85361
    May 12 '16 at 12:13

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