Robust Optimization Under Objective Functional Uncertainty
Abstract
This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous function space to maximize the cost, and the outer problem finds the optimal decision in a Euclidean space to minimize the cost. A solution algorithm is designed to alternately generate the worst-case objective function at the current decision and the optimal decision for the current collection of objective functions. Using operator theory, we prove that this algorithm converges to the defined ``semi-global'' saddle point of the ObRO problem. In addition, we propose a numerical solver based on the piece-wise linearization (PWL) approximation of objective functions. The PWL approximate problem is proved to be numerically consistent with the original ObRO problem. The obtained results are applied to the degradation-aware battery charging scheduling in distribution networks.
Related
- A sequential quadratic programming method for optimization with expectation objective functions, deterministic inequality constraints and robust subproblems
- Adjustable Robust Optimization with Discrete Uncertainty
- From Dual Tracking to Clipping: Provably Faster Distributionally Robust Multi-Objective Optimization
- Constructing Data-Driven Budgeted Uncertainty Sets for Robust Optimization
- A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification
BibTeX
@misc{song2026robust,
title = {{Robust Optimization Under Objective Functional Uncertainty}},
author = {Yue Song and Yuxi Lu and Gang Li and Kairui Feng and Qi Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.18669},
eprint = {2605.18669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18669},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Robust Optimization Under Objective Functional Uncertainty
AU - Yue Song
AU - Yuxi Lu
AU - Gang Li
AU - Kairui Feng
AU - Qi Liu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2605.18669
UR - https://arxiv.org/abs/2605.18669
AB - This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous function space to maximize the cost, and the outer problem finds the optimal decision in a Euclidean space to minimize the cost. A solution algorithm is designed to alternately generate the worst-case objective function at the current decision and the optimal decision for the current collection of objective functions. Using operator theory, we prove that this algorithm converges to the defined ``semi-global'' saddle point of the ObRO problem. In addition, we propose a numerical solver based on the piece-wise linearization (PWL) approximation of objective functions. The PWL approximate problem is proved to be numerically consistent with the original ObRO problem. The obtained results are applied to the degradation-aware battery charging scheduling in distribution networks.
ER -