Optimal Self-Concordant Barriers for Quantum Relative Entropies
本文证明了多种量子相对熵和散度的上图的自然障碍函数具有自和谐性，且障碍参数最优，使得相关凸优化问题可直接用非对称锥的内点法求解，无需近似或提升技术。
.Quantum relative entropies are jointly convex functions of two positive definite matrices that generalize the Kullback–Leibler divergence and arise naturally in quantum information theory. In this paper, we prove self-concordance of natural barrier functions for the epigraphs of various quantum relative entropies and divergences. Furthermore we show that these barriers have optimal barrier parameters. These barriers allow convex optimization problems involving quantum relative entropies to be directly solved using interior point methods for nonsymmetric cones, avoiding the approximations and lifting techniques used in previous approaches. More generally, we establish the self-concordance of natural barriers for various closed convex cones related to the noncommutative perspectives of operator concave functions and show that the resulting barrier parameters are optimal.Keywordsself-concordant barrierconic programmingquantum relative entropiesinterior-point methodsMSC codes90C2552A2026B2581P17