"Reverse" portfolio optimization in Matlab

As shown here in MathWorks examples, given the returns and covariance matrix for a set of assets, we can find the optimal set of portfolio weights that offers the lowest risk for a target return using standard mean variance optimization techniques.

However, instead of solving for optimal weights, I want to reverse this problem and solve for returns - i.e for a given set of weights, what is the corresponding set of returns that would yield these weights if put into a mean variance optimizer? I assume the covariance matrix is known, and only want to solve for returns.

Is there a way to do this in Matlab? There doesn't seem to be any out of the box solution using the financial toolbox, so I am trying to use quadprog, but have not been able to get a solution working.

[Matt J]

what is the corresponding set of returns

Can you even assume the set of returns is unique?