Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

We show that under a separation property, a Q-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Fernando García-Castaño and Miguel Ángel Melguizo-Padial acknowledge the financial support from the Spanish Ministry of Science, Innovation and Universities (MCIN/AEI) under grant PID2021-122126NB-C32, co-funded by the European Regional Development Fund (ERDF) under the slogan “A way of making Europe”

Denting points of convex sets and weak property (π) of cones in locally convex spaces

In this paper we first extend from normed spaces to locally convex spaces some characterizations of denting points in convex sets. On the other hand, we also prove that in an infrabarreled locally convex space a point in a convex set is denting if and only if it is a point of continuity and an extreme point of the closure of such a convex set under the strong topology in the second dual. The version for normed spaces of the former equivalence is new and contains, as particular cases, some known and remarkable results. We also extend from normed spaces to locally convex spaces some known characterizations of the weak property (π) of cones. Besides, we provide some new results regarding the angle property of cones and related. We also state that the class of cones in normed spaces having a pointed completion is the largest one for which the vertex is a denting point if and only if it is a point of continuity. Finally we analyse and answer several problems in the literature concerning geometric properties of cones which are related with density problems into vector optimization.The authors Fernando García-Castaño and M. A. Melguizo Padial have been supported by MINECO and FEDER (MTM2017-86182-P)

Management of biliary anastomotic strictures after liver transplantation (BASALT study): A nationwide Italian survey

Anastomotic stricture (AS) can occur in 10%-30% ofliver transplantation (LT) patients leading to liver dysfunction. Its diagnostic workup does not rely on a standard protocol or any international consensus of experts, thus AS management can considerably differ among centers. This affects the selection of patients after LT for endotherapy and, ultimately, results. Endotherapy is considered the reference standard treatment for AS,(2,3) but approach differs among centers depending on local expertise. The aim of the present retrospective survey was to report both the volume of endoscopic retrograde cholangiopancreatographies (ERCPs) dedicated to duct-to-duct AS treatment and the extent of variability in the management of AS at the Italian units involved in endotherapy of LT patients

Endo-therapies for biliary duct-to-duct anastomotic stricture after liver transplantation: outcomes of a nationwide survey

The most appropriate endo-therapeutic approach to biliary anastomotic strictures is yet to be defined