An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones
利用广义幂锥、幂均值锥和相对熵锥的Hessian矩阵低秩稀疏性质，实现内点法并证明增广线性系统可稀疏准定，通过稀疏LDL分解提升效率。
Abstract We present an implementation of interior-point methods for generalized power cones, power mean cones and relative entropy cones, by exploiting underlying low-rank and sparsity properties of the Hessians of their logarithmically homogeneous self-concordant barrier functions. We prove that the augmented linear system in our interior-point method can be sparse and quasidefinite after adding a static regularization term, enabling the use of sparse LDL factorization for nonsymmetric cones. Numerical results show that our implementation can exploit sparsity in our test examples.