To implement a number of pseudospectral and other algorithms, I often require several libraries:

High quality autodifferentiation (AD) capable of supporting thousands or hundreds of thousands of variables (with a high degree of sparsity, of course). Support for sparsity patterns is essential.

Constrained nonlinear least squares (or at least a constrained nonlinear optimizer), also capable of handling big sparse systems

Polynomial basis and quadrature (in one or two dimensions)
In Matlab, the answer is clear: the commericial Tomlab library has AD and wrappers to highquality commerical optimizers like Knitro, NPSOL, etc. CompEcon provides quadrature rules and basis matrices.
What are the appropriate python libraries for this that are of commerical quality with comprehensive tests and easy installation with conda/etc.:

AD: Many of the libraries, like Theano, work on symbolic expressions, which wonāt work here. I found https://github.com/HIPS/autograd/ but it seems that tensorflow also has an AD implementation (as far as I can tell). Gradients and Jacobians are essential for my immediate requirements, and Hessians are essential in general.

Constrained nonlinear least squares: I may have hundreds of thousands of variables with high sparsity and linear constraint so a high quality library is essential. I didnāt have much luck with Ipopt on a previous projects, for example, with led me to license knitro/npsol.

Constrained Optimizer: More generally for other problems, what are the nonlinear optimizers people have had luck with in the python ecosystem that can handle big problems?

Polynomial Basis: In particular one or twodimensional chebyshev polynomials. For python, do people use SciPy for this (e.g. https://docs.scipy.org/doc/numpy/reference/routines.polynomials.chebyshev.html ) It was unclear from the documentation how you would get a basis matrix and the Differentiation Matrix if this is the library people use.

Quadrature: Chebyshev, Laguerre, and GaussLobatto quadrature weights and rules. Also, I see https://docs.scipy.org/doc/numpy/reference/routines.polynomials.chebyshev.html routines, but couldnāt find GaussLobatto. What about https://pypi.python.org/pypi/quadpy ?
Thanks for any thoughts. More generally, I think it would be very valuable to collect a curated list of libraries for QuantEcon so economists stop writing (and insufficiently testing) so much of their own code from scratch.