OpenOpt is a framework for numerical optimization, nonlinear equations and systems of them. Part of it is licensed under the open sourceBSD license, but it uses proprietary software for some of its functionality and its stochastic optimization add-on is proprietary as well. Originally developed in MATLAB, OpenOpt is now developed in Python, using NumPy for numerical work.
OpenOpt-connected solvers can have any type of license, but are primarily open source and OSI-approved ones such as GPL, LGPL, and BSD.
Models written in FuncDesigner (another software package by the same team of developers) can be optimized with first derivatives obtained via automatic differentiation. Also, it can be used more like a language of mathematical formulas, possibly with recursive import of variables/formulas from other files. Both OpenOpt and FuncDesigner can solve constrained large-scale problems involving sparse matrices.