Characterizing properties of approximate solutions for optimization problems

Approximate solutions for optimization problems become of interest if the ' true' optimum cannot be found: this may happen for the simple reason that a n optimum does not exist or because of the 'bounded rationality' (or bounde d accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. in particula r we consider invariance properties. We prove that, where the domain contai ns optimization problems without maximum, there is no non-trivial consisten t solution satisfying non-emptiness, translation and multiplication invaria nce. Moreover, we show that the class of 'satisficing' solutions is obtaine d. if the invariance axioms are replaced with Chernoff's Choice Axiom. (C) 2000 Elsevier Science B.V. All rights reserved.