Robust Bilevel Optimization for Near-Optimal Lower-Level Solutions
Year: 2019
Type: preprint
Abstract: Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.
Source: arXiv (Cornell University)
Institution: Zuse Institute Berlin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4318070895