δ -perturbation of bilevel optimization problems: An error bound analysis
Year: 2024
Type: article
Abstract: In this paper, we analyze a perturbed formulation of bilevel optimization problems, which we refer to as δ-perturbed formulation. The δ-perturbed formulation allows to handle the lower level optimization problem efficiently when there are multiple lower level optimal solutions. By using an appropriate perturbation strategy for the optimistic or pessimistic formulation, one can ensure that the lower level optimization problem contains only a single (approximate) optimal solution for any given upper level decision. The optimistic or the pessimistic bilevel optimal solution can then be efficiently searched by algorithms that rely on solving the lower level optimization problem multiple times during the solution procedure. The δ-perturbed formulation is arrived at by adding the upper level objective function to the lower level objective function after multiplying the upper level objective by a small positive/negative δ. We provide a proof that the δ-perturbed formulation is approximately equivalent to the original optimistic or pessimistic formulation, along with an error bound for the approximation. We apply this scheme to a class of algorithms that attempts to solve optimistic and pessimistic variations of bilevel optimization problems by repeatedly solving the lower level optimization problem.
Source: Operations Research Perspectives
Authors: Margarita Antoniou, Ankur Sinha, Gregor Papa
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,440
OpenAlex ID: W4402082603