On Robustness in Nonconvex Optimization with Application to Defense Planning
Abstract
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%. Therefore, the derived expressions for subgradients and local Lipschitz moduli may accurately inform analysts about the possibility of obtaining cost-effective, parameter-robust decisions in nonconvex optimization.
Cite
@article{arxiv.2208.09725,
title = {On Robustness in Nonconvex Optimization with Application to Defense Planning},
author = {Johannes O. Royset},
journal= {arXiv preprint arXiv:2208.09725},
year = {2022}
}