Pseudo centre and its applications (Q2215631)

This paper considers the notion of a ``pseudo centre'' of a bounded region in \({\mathbb R}^{n}\). The idea is to replace the notion of a single center -- as the center of a circle -- with a finite set of points each of which forms a ``center'' for part of the boundary of the region. In the case of extreme values of a function on the boundary of such a region the paper uses pseudo centers to define what the authors call a depth diagram related to constrained optimum problems and which traces the value of the function on the boundary. The authors provide two helpful and extended examples to illuminate the depth diagram concept. The authors propose that computer algorithms to determine pseudo centers would be a profitable line of research.