Zeroth- and First-Order Methods for Bilevel Optimization
Abstract
Bilevel optimization (BO), also known as two-level optimization, is a critical branch of mathematical optimization. It involves two distinct optimization problems- an upper-level problem representing the decisions of a leader, and a lower-level problem representing the decisions of a follower. These problems are inherently connected, with solutions from one level influencing the other, creating a hierarchical and dynamic structure of decision-making. Numerous decision problems arising in DoD scenarios, such as resource allocation, logistics, radar system deployment, and engineering design, often exhibit a hierarchical structure and can be addressed as BO problems. However, solving BO is generally challenging due to its nested nature and the simultaneous consideration of multiple objectives and constraints. Additionally, it frequently involves sophisticated objective functions and constraints at both levels. Moreover, BO problems are often large-scale, especially in the big data era, characterized by objective functions and constraints involving a plethora of functions. To address these challenges, the research will develop novel computational methods to solve a broad spectrum of important and challenging BO problems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410343
Entities
People
- Zhaosong Lu
Organizations
- Air Force Office of Scientific Research
- Regents of the University of Minnesota
- United States Air Force