Globalized Robust Optimization for Nonlinear Uncertain Inequalities

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem’s parameters. The classical robust counterpart (RC) of the problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set, and offers no guarantees for parameter values outside this uncertainty set. The globalized
robust counterpart (GRC) extends this idea by allowing controlled constraint
violations in a larger uncertainty set. The constraint violations are controlled by
the distance of the parameter to the original uncertainty set. We derive tractable
GRCs that extend the initial GRCs in the literature: our GRC is applicable to
nonlinear constraints instead of only linear or conic constraints, and the GRC
is more flexible with respect to both the uncertainty set and distance measure
function, which are used to control the constraint violations. In addition, we
present a GRC approach that can be used to provide an extended trade-off
overview between the objective value and several robustness measures.