Differential Characterizations of Nonconical Dominance in Multiple Objective Decision Making

Suppose a decision maker's preferences are represented by an unknown value function v. Prior information concerning v (in the form of structural assumptions or revealed preferences) may serve to restrict v to some class V of value functions. An alternative y is dominated by an alternative z if v(y) < v(z) for (almost) every v ∈ V, in which case we write y <_Vz. Continuous variable problems are considered, in which alternatives are sought which are undominated under <_V. For these problems we derive necessary and sufficient differential optimality conditions of the Kuhn-Tucker type. An example is presented in which V is a class of measurable value functions of the multiplicative form introduced by Dyer and Sarin. Since <_V may be a nonconical order, these results are not subsumed by conventional vector optimization.