We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

Preference: Oral presentation

The irrigation problem is the problem of nding an e cient way to transport a measure μ onto a measure μ−. By e cient, we mean that a structure that achieves the transport (which, following [3], we call tra c plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper...

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice, and pa...

It is proved that every function of finite Baire index on a separable metric space K is a D-function, i.e., a difference of bounded semi-continuous functions on K. In fact it is a strong D-function, meaning it can be approximated arbitrarily closely in D-norm, by simple D-functions. It is shown that if the n derived set of K is non-empty for all finite n, there exist D-functions on K which are ...

Collaborative filtering plays the key role in recent recommender systems. It uses a user-item preference matrix rated either explicitly (i.e., explicit rating) or implicitly (i.e., implicit feedback). Despite the explicit rating captures the preferences better, it often results in a severely sparse matrix. The paper presents a novel iterative semi-explicit rating method that extrapolates unrate...

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.