Based on a “monotonicity” analogue of the l’Hospital Rule, monotonicity properties of the relative error are established for a Padé approximation of Mills’ ratio.

In this paper we discuss different monotonicity definitions applied in stochastic modelling and discuss the relationships between them. Obviously, the monotonicity concept depends on the relation order that we consider on the state space. In the case of total ordering the stochastic monotonicity used in stochasticmodelling and the realizablemonotonicity used in perfect simulation are equivalent...

We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f : E' -+ E, where E and E are finite ordered sets, the test always accepts a monotone f and rejects f with high probability if it is e-far from being monotone (i.e., if every monotone function differs from f on more than an E fraction of the domain). For any E > 0, the q...

We present a (randomized) test for monotonicity of Boolean functions. Namely, given the ability to query an unknown function at arguments of its choice, the test always accepts a monotone , and rejects with high probability if it is -far from being monotone (i.e., every monotone function differs from on more than an fraction of the domain). The complexity of the test is ! #" %$ . The analysis o...

We prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problem over a general closed convex set. Sufficient conditions for the strong monotonicity of their perturbed versions are also shown. These results include some known ones in the literature as particular instances. Inspired by these results, we ...

On the domain of cooperative transferable utility games, we investigate if there are single valued solutions that reconcile rationality, consistency and monotonicity (with respect to the worth of the grand coalition) properties. This paper collects some impossibility results on the combination of core selection with either complement or projected consistency, and core selection, max consistency...

General framework for proximal point algorithms based on the notion of (A, η)-maximal monotonicity (also referred to as (A, η)monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent correspo...

Amethod for using monotonicity information in multivariate Gaussian process regression and classification is proposed. Monotonicity information is introduced with virtual derivative observations, and the resulting posterior is approximated with expectation propagation. Behaviour of the method is illustrated with artificial regression examples, and the method is used in a real world health care ...

Pseudo-monotonicity seems to be a good notion to deal with convergence in non-linear terms of partial differential equations. J.-L. Lions [16] used two different definitions of pseudo-monotonicity for elliptic and parabolic problems, and derived associated existence results. Nonlinear elliptic-parabolic equations are intermediate equations for which an intermediate pseudo-monotonicity is define...