Can Bayesian Optimization be used in lieu of LP, QP, or MIP?

Is it possible to use Bayesian Optimization as a generic solver for traditional constrained optimization problems like LP, QP, MIP, etc...or it is it limited in scope to Hyperparameter search and auto-ML problems?

Bayesian Optimization has the advantage that it can be used on an arbitrary function $$f(x)$$ that can only be computed in black-box fashion. It has the disadvantage that it fails to make any use of known structure in the objective function or constraints.