Convex optimization on CAT(0) cubical complexes

We consider geodesically convex optimization problems involving distances to a finite set of points A in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in A. We propose a decomposition approach relying on standard Euclidean … Read more

Distributionally Robust Facility Location with Bimodal Random Demand

In this paper, we consider a decision-maker who wants to determine a subset of locations from a given set of candidate sites to open facilities and accordingly assign customer demand to these open facilities. Unlike classical facility location settings, we focus on a new setting where customer demand is bimodal, i.e., display, or belong to, … Read more