Stadium norm and Douglas-Rachford splitting: a new approach to road\n design optimization

2014/09/29 by Heinz H. Bauschke, Bauschke, Heinz H., Valentin Koch +3
Computer Science · Decision Sciences · Engineering · Mathematics · #49M27 #49M37 #52A21 #90C25 #Advanced Optimization Algorithms Research #Asphalt Pavement Performance Evaluation #FOS: Mathematics #Infrastructure Maintenance and Monitoring #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 65K05 #Probabilistic and Robust Engineering Design #Secondary 41A65

paper · pdf · doi:10.48550/arxiv.1409.8244

openalex publication_date 2014/09/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

The basic optimization problem of road design is quite challenging due to a\nobjective function that is the sum of nonsmooth functions and the presence of\nset constraints. In this paper, we model and solve this problem by employing\nthe Douglas-Rachford splitting algorithm. This requires a careful study of new\nproximity operators related to minimizing area and to the stadium norm. We\ncompare our algorithm to a state-of-the-art projection algorithm. Our numerical\nresults illustrate the potential of this algorithm to significantly reduce cost\nin road design.\n

Citations

• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Benchmarking optimization software with performance profiles

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