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Error bounds are a requisite for trusting or distrusting solutions in aninformed way. Until recently, provable error bounds in the absence ofconstraint qualifications were unattainable for many classes of cones that donot admit projections with known succinct expressions. We build such errorbounds for the generalized power cones, using the recently developed frameworkof one-step facial residual functions. We also show that our error bounds aretight in the sense of that framework. Besides their utility for understandingsolution reliability, the error bounds we discover have additional applicationsto the algebraic structure of the underlying cone, which we describe. Inparticular we use the error bounds to compute the dimension of the automorphismgroup for the generalized power cones, and to identify a set of generalizedpower cones that are self-dual, irreducible, nonhomogeneous, and perfect

Generalized power cones: optimal error bounds and automorphisms