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http://hdl.handle.net/10397/106714
Title: | Generalized power cones : optimal error bounds and automorphisms | Authors: | Lin, Y Lindstrom, SB Louren, BF Pong, TK |
Issue Date: | 2024 | Source: | SIAM journal on optimization, 2023, v. 34, no. 2, p. 1316-1340 | Abstract: | Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until recently, provable error bounds in the absence of constraint qualifications were unattainable for many classes of cones that do not admit projections with known succinct expressions. We build such error bounds for the generalized power cones, using the recently developed framework of one-step facial residual functions. We also show that our error bounds are tight in the sense of that framework. Besides their utility for understanding solution reliability, the error bounds we discover have additional applications to the algebraic structure of the underlying cone, which we describe. In particular we use the error bounds to compute the automorphisms of the generalized power cones, and to identify a set of generalized power cones that are self-dual, irreducible, nonhomogeneous, and perfect. | Keywords: | Facial residual functions Generalized power cones Hölderian error bounds Irreducible cones Nonhomogeneous cones Perfect cones |
Publisher: | Society for Industrial and Applied Mathematics Publications | Journal: | SIAM journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/22M1542921 | Rights: | Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The following publication Lin, Y., Lindstrom, S. B., Lourenço, B. F., & Pong, T. K. (2024). Generalized Power Cones: Optimal Error Bounds and Automorphisms. SIAM Journal on Optimization, 1316-1340 is available at https://doi.org/10.1137/22M1542921. |
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