A duality between the metric projection onto a convex cone and the metric projection onto its dual

AbstractIf K and L are mutually dual pointed convex cones in Rn with the metric projections onto them denoted by PK and PL respectively, then the following two assertions are equivalent: (i) PK is isotone with respect to the order induced by K (i.e. v−u∈K implies PKv−PKu∈K); (ii) PL is subadditive with respect to the order induced by L (i.e. PLu+PLv−PL(u+v)∈L for any u,v∈Rn)