Thanks to Tom Cools' suggestion, I found out how to do it. In the resource class:

        @Inject
        private ConstraintMetaModel constraintMetaModel;

        @GET
        @Path("constraints")
        @Produces(MediaType.APPLICATION_JSON)
        public Collection<String> listConstraintNames() {
                return constraintMetaModel.getConstraints().stream().map(Constraint::getConstraintRef)
                                .map(ConstraintRef::constraintName).collect(Collectors.toSet());
        }