Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach

Elisa Caprari (), Lorenzo Cerboni Baiardi () and Elena Molho ()
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Elisa Caprari: University of Pavia
Lorenzo Cerboni Baiardi: University of Bologna
Elena Molho: University of Pavia

Journal of Global Optimization, 2022, vol. 84, issue 2, No 2, 295-320

Abstract: Abstract The robust optimization approach can be used to tackle uncertain vector problems by considering worst case scenarios. In this context, notions of robust efficient solutions which are coherent with a set-valued minimization process have been introduced in literature in order to avoid unduly pessimistic attitudes (see e.g. Ehrgott et al. in Eur. J. Oper. Res. 239(1), 17–31, 2014). We address the question whether scalarization and robustification can be commuted in a non componentwise framework. We prove that the commutation of the two approaches is ensured under appropriate assumptions. To this purpose, we identify a class of scalarization processes that ensure necessary and sufficient robust optimality conditions through the direct scalarization of the uncertain vector optimization problem, without explicitly passing through the set-valued formulation of the problem.

Keywords: Vector optimization; Robust optimization; Scalarization; Uncertainty (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01142-2

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