In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov (Optim Methods Softw 27(4–5): 893–917, 2012) introduced a 4-self-concordant barrier for the power cone, also known as Koecher’s cone. In his PhD thesis, Chares (Cones and interior-point algorithms for structured convex optimization involving powers and exponentials, PhD thesis, Universite catholique de Louvain, 2009) found an improved 3-self-concordant barrier for the power cone. In addition, he introduced the generalized power cone, and conjectured a “nearly optimal” self-concordant barrier for it. In this paper, we prove Chares’ conjecture. As a byproduct of our analysis, we derive a self-concordant barrier for a nonnegative power cone.

在非对称圆锥优化的内点方法及其应用的研究中，Nesterov (Optim Methods Softw 27(4-5): 893-917, 2012) 为功率圆锥引入了 4-self-concordant 势垒，也称为Koecher锥体。在他的博士论文中，Chares（用于涉及幂和指数的结构化凸优化的锥体和内点算法，博士论文，鲁汶大学，2009 年）发现了功率锥的改进的 3-自协调屏障。此外，他还引入了广义功率锥，并为其推测了一个“近乎最优”的自谐屏障。在本文中，我们证明了 Chares 猜想。作为我们分析的副产品，我们推导出了非负功率锥的自调屏障。