# K-Adaptability in Two-Stage Mixed-Integer Robust Optimization

arXiv: https://arxiv.org/abs/1706.07097 · HTML: https://mlsanity.com/paper/1706.07097/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 6 of 6)

- [A Framework for Inherently Interpretable Optimization Models](https://mlsanity.com/paper/2208.12570/) (2022)
- [Machine Learning for K-adaptability in Two-stage Robust Optimization](https://mlsanity.com/paper/2210.11152/) (2022)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Balls](https://mlsanity.com/paper/2407.13625/) (2024)
- [Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty](https://mlsanity.com/paper/2605.14494/) (2026)
- [Optimizing Minimax Regret in Uncertain MDPs with Small Sets of Policies](https://mlsanity.com/paper/2608.02509/) (2026)

## Abstract (arXiv)

We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying a K-adaptability formulation that selects K candidate recourse policies before observing the realization of the uncertain parameters and that implements the best of these policies after the realization is known. We address the second challenge through a branch-and-bound scheme that enjoys asymptotic convergence in general and finite convergence under specific conditions. We illustrate the performance of our algorithm in numerical experiments involving benchmark data from several application domains.