An Efficient IPM Implementation for A Class of Nonsymmetric Cones

We present an efficient implementation of interior point methods for a family of nonsymmetric cones, including generalized power cones, power mean cones and relative entropy cones, by exploiting underlying low-rank and sparse properties of Hessians of homogeneous self-concordant barrier functions. We prove that the augmented linear system in our interior point method is sparse and quasi-definite, enabling the use of sparse LDL factorization with a dual scaling strategy for nonsymmetric cones. Numerical results show that our proposed implementation for nonsymmetric cones performs much faster than the state-of-art solvers for spare problems and scales well for large problems.