Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.

Maria-Antònia Oliver o el plaer de narrar en femení

Maria-Antònia Oliver és una figura cabdal en la història de la novel·la policíaca en llengua catalana. Amb un personatge principal innovador en el panorama literari català dels anys vuitanta, Oliver destaca per una sèrie d’aspectes com són el seu personatge principal, feminista i representant del hard-boiled i la forta crítica social, especialment centrada en l’illa de Mallorca, aspectes que són objecte d’estudi en aquest article. Temes com el feminisme, l’impacte social del turisme o la situació de la llengua catalana a les Balears formen part de les seves obres i demostren el compromís social de l’autora mallorquina.