Γ-uncertainties have been introduced for adjusting the degree of conservatism of
robust counterparts of (discrete) linear optimization problems under interval uncertainty. This
article’s contribution is a generalization of this approach to (mixed-integer) nonlinear optimization
problems. We focus on the cases in which the uncertainty is linear but also derive formulations
for the general case. We present cases where the robust counterpart of a nonlinear combinatorial
problem is solvable with a polynomial number of oracle calls for the underlying nominal problem
and elaborate on it using a quadratic assignment problem. We show the computational efficiency
with a numerical study tackling a patient transport problem and the quadratic assignment
problem.
Article
View Γ-counterparts for robust nonlinear combinatorial and discrete optimization