Thank you for your interest Andrew.
variable transformations to form unconstrained problems from bound constrained problems
I am considering writing a new transformation function to calculate the equations on that web page that you linked to discussing variable transformations. If it is as straight-forward as I think it will be to write, then I may also do some comparisons between the "clipping" method and the sin() / arcsin() / sqrt() method you highlighted. As an aside, I was told informally about the existence of that method you referenced during a conversation I had last week, but I have been finding it very difficult to find any written discussion (i.e. actual analytical expressions) about that method via web searches before I made the proposals. So thank you very much for linking that web page - it is very useful information for my own personal work as well as the proposed Scipy modifications!
user-specified objective function values for points in the user-specified initial simplex
I have indeed used a keyword in the manner you describe (and therefore similar in style to the initial_simplex keyword) - it seemed to me to be a "clean" way of implementing this modification and very straightforward to implement since it is so similar to the initial_simplex handling.
evaluation budget count check
I am thinking of writing checks which will effectively skip the execution of the remainder of the solver algorithm if the budget has been met, before finally sorting the current simplex of evaluations and returning the best. My inclination is to avoid using StopIteration since it is an exception i.e. it suggests some kind of problem has occurred, where as my proposed idea is to handle evaluations up to the exact budget as a feature. Anyway I haven't yet made an attempt on this modification, so my thoughts are tentative and may change - especially if it turns out that I am trying to write spaghetti. dickson