Adelhütte D, Liers F (2021)
Publication Language: English
Publication Type: Other publication type
Publication year: 2021
URI: http://www.optimization-online.org/DB_HTML/2020/05/7806.html
Open Access Link: http://www.optimization-online.org/DB_HTML/2020/05/7806.html
Γ–uncertainty sets have been introduced for adjusting the degree of conservatism of robust
counterparts of (discrete) linear programs. The contribution of this paper is a generalization
of this approach to (mixed–integer) nonlinear optimization programs. We focus on the cases in
which the uncertainty is linear or concave but also derive formulations for the general case. By
applying reformulation techniques that have been established for nonlinear inequalities under
uncertainty, we derive equivalent formulations of the robust counterpart that are not subject
to uncertainty. The computational tractability depends on the structure of the functions
under uncertainty and the geometry of its uncertainty set. We present cases where the robust
counterpart of a nonlinear combinatorial program is solvable with a polynomial number of
oracle calls for the underlying nominal program. Furthermore, we present robust counterparts
for practical examples, namely for (discrete) linear, quadratic and piecewise linear settings.
APA:
Adelhütte, D., & Liers, F. (2021). Γ–counterparts for robust nonlinear combinatorial and discrete optimization.
MLA:
Adelhütte, Dennis, and Frauke Liers. Γ–counterparts for robust nonlinear combinatorial and discrete optimization. 2021.
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