arXiv subjects

Paolo d'Alessandro

Publications and source records attributed to Paolo d'Alessandro.

2 recordsLinked to original sources

arXiv2023

Support, Convexity Conditions and Convex Hypersurfaces in Infinite Dimension

Working in infinite dimensional linear spaces, we deal with support for closed sets without interior. We generalize the Convexity Theorem for closed sets without interior. Finally we study the infinite dimensional version of Jordan hypersurfaces. Our whole work never assumes smoothness and is based exclusively on non-differential Convex Analysis tools and, in particular, on theory of convex cones. A crucial mathematical tool for our results is obtained solving the decomposition problem for non-closed non pointed cones.

math.FA↗

arXiv2003

A new conical internal evolutive LP algorithm

In a previous paper, published in 1992, a primal conical LP algorithm with exact finite coonvergence was presented. The underlying optimality condition requires tangency of two sets (an affine space and a cone). In the algorithm the two sets remain disjoint until the last step. This left open the possibility of developing an internal algorithm in which, by the contrary, the two sets keep intersecting each other. Such an algorithm along with a new optimality condition is presented here. It is stressed that the results given here complete the picture of the conical approach to LP in many other important respect, as illustrated in detail in the introduction.

math.OC↗