Ordinal optimization

In mathematical optimization, ordinal optimization is the maximization of functions taking values in a partially ordered set ('poset'). Ordinal optimization has applications in the theory of queuing networks. In mathematical optimization, ordinal optimization is the maximization of functions taking values in a partially ordered set ('poset'). Ordinal optimization has applications in the theory of queuing networks. A partial order is a binary relation '≤' over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b, and c in P, we have that: In other words, a partial order is an antisymmetric preorder. A set with a partial order is called a partially ordered set (also called a poset). The term ordered set is sometimes also used for posets, as long as it is clear from the context that no other kinds of orders are meant. In particular, totally ordered sets can also be referred to as 'ordered sets', especially in areas where these structures are more common than posets. For a, b distinct elements of a partially ordered set P, if a ≤ b or b ≤ a, then a and b are comparable. Otherwise they are incomparable. If every two elements of a poset are comparable, the poset is called a totally ordered set or chain (e.g. the natural numbers under order). A poset in which every two elements are incomparable is called an antichain.