LogMIP can solve linear/nonlinear disjunctive hybrid models that follow the formulation showed. Disjunctive models are those where discrete decisions are written only in the form of disjunctions, while hybrid models involve both disjunctions and mixed-integer constraints. According to the user model type (linear or non-linear), by default, LogMIP decides the solver to run. The user can also specify the model type by including the following sentence in the LogMIP section:

modeltype [MIP|MINLP]

The specifics solvers would be explained in the following sections of the site: