SigOpt allows specifying constraint ranges for every parameter. If the parameter space isn't a tensor product you can report constraint violating suggestions as failures via our API [1] and SigOpt will take that into account as it optimizes.
SigOpt isn't a constraint optimization package for solving things like k-SAT thought if that is what you were asking.
In addition to bounds, say I'd like to solve a problem where the variables must satisfy a linear or nonlinear system of equations. So overall there are fewer degrees of freedom than the number of variables, but the problem structure is such that it may be much more efficient to express the objective function and constraints in terms of the higher-dimensional space.
This is where the reporting of "failures" as mentioned above can be helpful. Any suggestion that violates your system of equations based constraints can be instantly reported as a "failure," and this will be taken into account as SigOpt converges to the best parameters.
You could also try to bake this into the objective function (with an L2 penalty for how bad it violates some constraints), depending on how hard the constraints of the problem actually are.
Equality constraints means you're working in a lower-dimensional subspace, I'd have to find out more about your algorithms but I'd be surprised if you wound up evaluating many feasible points at all (esp. with nonlinear equalities).
L2 penalty would likely converge to an infeasible solution. Augmented Lagrangian would be better, but then you're making users handle dual updates. At that point I'd rather use an actual constrained optimization library that does the algorithm carefully, and use primal-dual interior point. Not having this kind of thing built in counts as "no constrained optimization" IMO.
