Stadium Norm and Douglas-Rachford Splitting: A New Approach to Road Design Optimization
Heinz H. Bauschke, Valentin R. Koch, Hung M. Phan
Operations Research · 2016 · Volume 64 · Issue 1
Abstract
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.
Keywords
convex function, convex set, Douglas-Rachford algorithm, Fenchel conjugate, intrepid projector, method of cyclic intrepid projections, norm, projection, projector, proximal mapping, proximity operator, road design, stadium norm
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