Complexity of near-optimal robust versions of multilevel optimization problems

TL;DR

This paper investigates the computational complexity of near-optimal robust multilevel optimization problems, showing that their complexity remains unchanged under broad conditions when robustness is modeled through adversarial decision-makers.

Contribution

It provides a complexity analysis demonstrating that near-optimal robustness does not increase the computational difficulty of multilevel problems in general.

Findings

Near-optimal robustness preserves the original complexity class.

Modeling robustness with adversarial decision-makers maintains problem complexity.

Complexity results apply broadly under general conditions.

Abstract

Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.