Metric and Spectral Geometric Means on Symmetric Cones

摘要: In a development of ecient primal-dual interior-points algorithms for self- scaled convex programming problems, one the important properties such cones is existence and uniqueness "scaling points". this paper through identification scaling points with notion "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical Lowner-Heinz inequality, Ando Jensen Furuta inequality) to cones. We also develop theory spectral means which has recently appeared in linear monotone complementarity problem domains associated derive Nesterov-Todd inequality using property