Convexification of extremely nonconvex compositions with norms
Abstract
Mathematical optimization problems involving the distances between objects arise in a variety of settings. For instance, in the obnoxious facility location problem, communities experience disutility depending on their distance from facilities, such as noise from airports or pollution from industrial plants. Current algorithms are unable to find the optimal locations of more than five facilities. Similar challenges exist for problems of packing objects into containers and even molecular-structure determination problems. This effort seeks new, more efficient theory and algorithms for solving such problems. The proposed work will develop new mathematical optimization techniques that will make it possible to solve realistic problem sizes to guaranteed optimality for problems involving distances between objects. To achieve this goal, the proposed work will develop closed-form mathematical expressions of functions required to obtain rigorous pessimistic and optimistic approximations of decision outcomes. These approximations will facilitate domain decomposition algorithms for obtaining optimal solutions for a broad class of problems for the first time.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310345
Entities
People
- Nikolaos Sahinidis
Organizations
- Air Force Office of Scientific Research
- Georgia Tech Research Corporation
- United States Air Force