Constrained optimization problems under uncertainty with coherent lower previsions

• DOI: 10.1016/j.fss.2012.02.004
• Publication Date: 2012-02-13T18:55:15Z
• Authors: Erik Quaeghebeur; Keivan Shariatmadar; Gert de Cooman
• Keywords: PROBABILITIES; Technology; Maximality; Science & Technology; Linear prevision; BEHAVIORAL-MODEL; Statistics & Probability; NUMERICAL POSSIBILITY THEORY; Mathematics, Applied; 02 engineering and technology; DECISION-MAKING; FUZZY; Mathematics and Statistics; Computer Science, Theory & Methods; Physical Sciences; Computer Science; 0202 electrical engineering, electronic engineering, information engineering; Possibility distribution; Coherent lower prevision; Constrained optimization; Maximinity; Mathematics; Vacuous prevision

We investigate a constrained optimization problem with uncertainty about constraint parameters. Our aim is to reformulate it as a (constrained) optimization problem without uncertainty. This is done by recasting the original problem as a decision problem under uncertainty. We give results for a number of different types of uncertainty models-linear and vacuous previsions, and possibility distributions-and for two common but different optimality criteria for such decision problems-maximinity and maximality. We compare our approach with other approaches that have appeared in the literature.