Does solving the following optimization problem : $ \min_A \text{Tr} [A \sigma] $ such that $ \text{Tr} [A^{-1} \rho] \leq 1 $ give the same solution as solving $ \min_A \text{Tr} [A \sigma]\text{Tr} [A^{-1} \rho] $?, where $\rho, \sigma \geq 0 $ and $\text{Tr } \rho= \text{Tr } \sigma=1 $, as they are density matrices. Thank you!

  • $\begingroup$ This is generally not how you roll constraints into a modified objective function. For inequality constraints, look into the Karush-Kuhn-Tucker conditions (which are more or less the generalization of Lagrange multipliers). $\endgroup$
    – Ian
    Jan 27, 2018 at 19:12
  • $\begingroup$ Yes, I understand this not how it is usually done, but I would like to know whether these two optimization problems are equivalent. $\endgroup$ Jan 27, 2018 at 19:16


You must log in to answer this question.

Browse other questions tagged .