Stadium Norm and Douglas-Rachford Splitting: A New Approach to Road Design Optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Bauschke, Heinz H.; Koch, Valentin R.; Phan, Hung M.
• 署名单位: University of British Columbia; Autodesk, Inc.; University of Massachusetts System; University of Massachusetts Lowell
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2015.1427
• 发表日期: 2016
• 页码: 201-218
• 关键词: algorithms

摘要

The basic optimization problem of road design is quite challenging due to an objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the Douglas-Rachford splitting algorithm. This requires a careful study of new proximity operators related to minimizing area and to the stadium norm. We compare our algorithm to a state-of-the-art projection algorithm. Our numerical results illustrate the potential of this algorithm to significantly reduce cost in road design.