In #21003, we added support for PySCIPOpt and added scip as a optional MILP-solver.
The solver SCIP can also handle nonlinear programs. There are also other nonlinear solvers available, such as Couenne from coin-or https://projects.coin-or.org/Couenne/.

I suggest to add a new class MixedIntegerNonlinearProgram, simliar to the
class MixedIntegerLinearProgram, which can handle nonlinear constraints. One can also think about special treatment for quadratic constraints, and possibly convex optimization.

For this new class, there should be a generic backend. As soon as this is ready, we can build on top of this ticket to get backends for scip and couenne.

Comments and suggestions welcome!

CC: @mkoeppe @yuan-zhou

Component: numerical

Issue created by migration from https://trac.sagemath.org/ticket/25116