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In the context of structured nonconvex optimization, we estimate the increasein minimum value for a decision that is robust to parameter perturbations ascompared to the value of a nominal problem. The estimates rely on detailedexpressions for subgradients and local Lipschitz moduli of min-value functionsin nonconvex robust optimization and require only the solution of the nominalproblem. The theoretical results are illustrated by examples from militaryoperations research involving mixed-integer optimization models. Across 54cases examined, the median error in estimating the increase in minimum value is12%. Therefore, the derived expressions for subgradients and local Lipschitzmoduli may accurately inform analysts about the possibility of obtainingcost-effective, parameter-robust decisions in nonconvex optimization.

On Robustness in Nonconvex Optimization with Application to Defense Planning