Characterizing centers of convex bodies via optimization (Q1332230)

The authors use optimization theory to introduce general planar center points as the solutions of minimization problems for certain sums or products of ``distance functions''. Many classical or more modern types of ``center'' are discussed from this point of view. In particular, the authors define logarithmic centers using logarithmic distance functions. They also give a vector characterization of these centers. Further, they investigate the concept of center points in higher dimensions.