Consider updating SLSQP to a modern and maintained implementation

Description of feature

Currently, the version of SLSQP provided is quite old, and suffers from several bugs that have been fixed elsewhere. See #301 for some discussion. Since SLSQP remains a rather popular optimizer, to maintain long term viability, I think it would be best to switch to using a version that is better maintained. This would also avoid any duplication in maintenance efforts.

Potential solution

As far as I'm aware, there are three versions out there:

• Scipy: well maintained and widely available, plus we already depend on scipy so there will be no additional dependencies. However seems to lack things such as fetching the optimal Lagrange multipliers that exist in pyOptSparse (though what we have might be broken, I don't really remember)
• slsqp: much more modern than the old F77 code, seems to be very well maintained. Lacks Python interface
• NLopt: given that it's built into an entire optimization framework, we will not consider this option further

This thread will serve as a place to discuss future plans regarding SLSQP.

Start by reviewing the current SLSQP implementation and the discussion in issue #301, then compare the SciPy and slsqp alternatives described here. Done means choosing a maintained implementation and agreeing how existing capabilities, including optimal Lagrange multipliers, will be preserved.