Calculus of Inequalities |

For example, myriad alternative systems of linear inequality can be explained in terms of pointed closed convex cones and their duals. As another example, the general first-order necessary and sufficient condition for optimality of a solution to a minimization problem, with real differentiable convex objective function, can be expressed as an inequality over a convex feasible set. For one last example from an infinitude, the Schoenberg criterion for determining existence of a Euclidean distance matrix is accurately interpreted as a discretized membership relation (a generalized inequality) between the EDM cone and its ordinary dual. |