论文标题
广义功率锥：最佳误差界限和自动形态
Generalized power cones: optimal error bounds and automorphisms
论文作者
论文摘要
错误范围是以知情方式信任或不信任解决方案的必要条件。直到最近，在没有约束资格的情况下，可证明的误差界限对于许多不接受已知简洁表达式预测的锥体的锥体无法实现。我们使用最近开发的一步面部残留功能的框架为广义功率锥构建了此类误差界。我们还表明，从该框架的意义上讲，我们的错误界限很紧。除了理解解决方案可靠性的实用性外，我们发现的错误界限还对基础锥体的代数结构有其他应用，我们将描述。特别是，我们使用错误范围来计算广义功率锥体的自动形态群的维度，并确定一组自偶有，不可估算，不合应性和完美的广义功率锥
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 dimension of the automorphism group for the generalized power cones, and to identify a set of generalized power cones that are self-dual, irreducible, nonhomogeneous, and perfect
