On Robustness in Nonconvex Optimization with Application to Defense Planning

08/20/2022

∙

by   Johannes O. Royset, et al.

∙

Naval Postgraduate School

∙

0

∙

share

In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed expressions for subgradients and local Lipschitz moduli of min-value functions in nonconvex robust optimization and require only the solution of the nominal problem. The theoretical results are illustrated by examples from military operations research involving mixed-integer optimization models. Across 54 cases examined, the median error in estimating the increase in minimum value is 12 moduli may accurately inform analysts about the possibility of obtaining cost-effective, parameter-robust decisions in nonconvex optimization.