Bounded optimization using the Hessian matrix (scipy)
l-bfgs-b does a bounded optimisation. Like any quasi-Newton method it approximates the Hessian. But this is often better than using the real Hessian.
I am trying to optimize a function of a small number of variables (somewhere from 2 to 10). What I am trying to do is calculate the minimum of the function on a bounded hypercube 
[0,1] x [0,1] x ... x [0,1]
The calculation of the function, its gradient and its hessian is al relatively simple, quick and accurate.
Now, my problem is this:
Using scipy, I can use either scipy.optimize.minimize(..., method='Newton-CG') or scipy.optimize.minimize(..., method='TNC') to calculate the minimum of the function, however:

The first method uses the Hessian matrix, but I cannot set the bounds for the variables I am optimizing
The second method allows me to set bounds on the variables, but the method does not use the Hessian.

Is there any method that will use both?