Resolution of dilemmas: A mathematical theory

A mathematical formulation for a dilemma (i.e. a situation in which a very difficult choice between two alternatives must be made) is given. Multiple-objective programming is assumed as the model for a single decision maker. It is shown that, in principle, any dilemma is resolvable. Furthermore, there is always more than one way in which to resolve a dilemma. Illustrative examples from non-convex optimization are presented.