James LARROUY (LAMIA) : An introduction to the Set Order Topology and its application to well-posedness in Set Optimization. The Portfolio Investment Problem : an example of practicability

In this work, we introduce a topology on the power set P(Z) of a partially ordered normed space Z from which we derive a topological convergence on P(Z) along with new concepts of continuity and semicontinuity for set valued mappings. Our goal is to propose an appropriate framework to address set optimization problems involving set relations based on a cone ordering. Taking advantage of this new setting, we establish several results regarding the well-posedness of set-valued optimization problems that are consistent with the state-of-the-art. We also show the practicability of this new theory through a well-posedness result for the portfolio investment problem obtained in our topological framework.