Tractable Approximation to Robust Nonlinear Production Frontier Problem

Robust optimization is a rapidly developing methodology for handling optimization problems affected by the uncertain‐but‐bounded data perturbations. In this paper, we consider the nonlinear production frontier problem where the traditional expected linear cost minimization objective is replaced by one that explicitly addresses cost variability. We propose a robust counterpart for the nonlinear production frontier problem that preserves the computational tractability of the nominal problem. We also provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.