Constrained optimization problems under uncertainty with coherent lower previsions

  • Authors:

  • Erik Quaeghebeur;Keivan Shariatmadar;Gert De Cooman

  • Affiliations:

  • Ghent University, SYSTeMS Research Group, EESA Department, Faculty of Engineering and Architecture, Technologiepark-Zwijnaarde 914, 9052 Zwijnaarde, Belgium;Ghent University, SYSTeMS Research Group, EESA Department, Faculty of Engineering and Architecture, Technologiepark-Zwijnaarde 914, 9052 Zwijnaarde, Belgium;Ghent University, SYSTeMS Research Group, EESA Department, Faculty of Engineering and Architecture, Technologiepark-Zwijnaarde 914, 9052 Zwijnaarde, Belgium

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

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.