In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions.

翻译：[中文摘要] 本文在不要求任何约束规格的条件下，建立了对数行列式锥（即对数行列式函数透视图的闭包）的紧致误差界。该误差界基于近期发展的单步面残差函数框架推导得到。