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A constrained optimization problem under uncertainty

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Abstract
We investigate a constrained optimization problem for which there is uncertainty about a constraint parameter. 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 different optimality criteria for decision problems under uncertainty—maximinity and maximality.
Keywords
possibility distribution, linear prevision, maximinity, maximality, vacuous prevision, constrained optimization

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Chicago
Quaeghebeur, Erik, Keivan Shariatmadar, and Gert De Cooman. 2010. “A Constrained Optimization Problem Under Uncertainty.” In World Scientific Proceedings Series on Computer Engineering and Information Science, ed. Da Ruan, Yianrui Li, Yang Xu, Guoqing Chen, and Etienne Kerre, 791–796. Singapore, Singapore: World Scientific.
APA
Quaeghebeur, E., Shariatmadar, K., & De Cooman, G. (2010). A constrained optimization problem under uncertainty. In Da Ruan, Y. Li, Y. Xu, G. Chen, & E. Kerre (Eds.), World Scientific Proceedings Series on Computer Engineering and Information Science (pp. 791–796). Presented at the 9th International FLINS conference on Foundations and Applications of Computational Intelligence (FLINS 2010), Singapore, Singapore: World Scientific.
Vancouver
1.
Quaeghebeur E, Shariatmadar K, De Cooman G. A constrained optimization problem under uncertainty. In: Ruan D, Li Y, Xu Y, Chen G, Kerre E, editors. World Scientific Proceedings Series on Computer Engineering and Information Science. Singapore, Singapore: World Scientific; 2010. p. 791–6.
MLA
Quaeghebeur, Erik, Keivan Shariatmadar, and Gert De Cooman. “A Constrained Optimization Problem Under Uncertainty.” World Scientific Proceedings Series on Computer Engineering and Information Science. Ed. Da Ruan et al. Singapore, Singapore: World Scientific, 2010. 791–796. Print.
@inproceedings{973379,
  abstract     = {We investigate a constrained optimization problem for which there is uncertainty about a constraint parameter. 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 different optimality criteria for decision problems under uncertainty---maximinity and maximality.},
  author       = {Quaeghebeur, Erik and Shariatmadar, Keivan and De Cooman, Gert},
  booktitle    = {World Scientific Proceedings Series on Computer Engineering and Information Science},
  editor       = {Ruan, Da and Li, Yianrui and Xu, Yang and Chen, Guoqing and Kerre, Etienne},
  isbn         = {9789073802872},
  keyword      = {possibility distribution,linear prevision,maximinity,maximality,vacuous prevision,constrained optimization},
  language     = {eng},
  location     = {Chengdu, PR China},
  pages        = {791--796},
  publisher    = {World Scientific},
  title        = {A constrained optimization problem under uncertainty},
  url          = {http://dx.doi.org/10.1142/9789814324700\_0120},
  year         = {2010},
}

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