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- Title
Polyhedral Approximation of Spectrahedral Shadows via Homogenization.
- Authors
Dörfler, Daniel; Löhne, Andreas
- Abstract
This article is concerned with the problem of approximating a not necessarily bounded spectrahedral shadow, a certain convex set, by polyhedra. By identifying the set with its homogenization, the problem is reduced to the approximation of a closed convex cone. We introduce the notion of homogeneous δ -approximation of a convex set and show that it defines a meaningful concept in the sense that approximations converge to the original set if the approximation error δ diminishes. Moreover, we show that a homogeneous δ -approximation of the polar of a convex set is immediately available from an approximation of the set itself under mild conditions. Finally, we present an algorithm for the computation of homogeneous δ -approximations of spectrahedral shadows and demonstrate it on examples.
- Subjects
CONVEX sets; APPROXIMATION error; POLYHEDRAL functions; ASYMPTOTIC homogenization; POLYHEDRA
- Publication
Journal of Optimization Theory & Applications, 2024, Vol 200, Issue 2, p874
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-023-02363-5