Maximum likelihood inference for log-linear models subject to constraints of double monotone dependence

To model an hypothesis of double monotone dependence between two ordinal categorical variables $A$ and $B$ usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined respectively on the conditional distributions of $A$ given $B$ and on the conditional distributions of $B$ given $A$ are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model.