We analyse the scaling matrix, search direction, and neighbourhood used in MOSEK's algorithm for nonsymmetric conic optimization [J. Dahl and E.D. Andersen, A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization, preprint (2019)]. It is proven that these can be used to compute a near-optimal solution to the homogeneous self-dual model in polynomial time. This provides a theoretical foundation for MOSEK's nonsymmetric conic algorithm. The main steps in the analysis are sandwiching MOSEK's scaling matrix between the primal and dual barrier's Hessians, and using this information to carefully check all the neighbourhood conditions after a small, improving step is taken.

我们分析了 MOSEK 非对称圆锥优化算法中使用的缩放矩阵、搜索方向和邻域 [J. Dahl 和 ED Andersen，用于非对称指数锥优化的原始对偶内点算法，预印本 (2019)]。事实证明，这些可用于在多项式时间内计算齐次自对偶模型的近似最优解。这为MOSEK的非对称圆锥算法提供了理论基础。分析的主要步骤是将 MOSEK 的缩放矩阵夹在原始和双重障碍的 Hessian 矩阵之间，并在采取小的改进步骤后使用此信息仔细检查所有邻域条件。