On robustness in nonconvex optimization with application to defense planning

We estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal nonconvex problem. The estimates rely on expressions for subgradients and local Lipschitz moduli of min-value functions and require only the solution of the nominal problem. Across 54 mixed-integer optimization models, the median error in estimating the increase in minimum value is 12%. The results inform analysts about the possibility of obtaining cost-effective, parameter-robust decisions.