A unified approach for different concepts of robustness and stochastic programming via non-linear scalarizing functionals

Author: Klamroth K.  

Publisher: Taylor & Francis Ltd

ISSN: 0233-1934

Source: Optimization, Vol.62, Iss.5, 2013-05, pp. : 649-671

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Abstract

We show that many different concepts of robustness and of stochastic programming can be described as special cases of a general non-linear scalarization method by choosing the involved parameters and sets appropriately. This leads to a unifying concept which can be used to handle robust and stochastic optimization problems. Furthermore, we introduce multiple objective (deterministic) counterparts for uncertain optimization problems and discuss their relations to well-known scalar robust optimization problems by using the non-linear scalarization concept. Finally, we mention some relations between robustness and coherent risk measures.