A Generic Primal-dual Interior-point Algorithm for Cone Optimization Based on Kernel Functions

Conic Optimization (CO) provides a new framework in the field of Optimization that includes linear, semidefinite, and second-order cone optimizations problems as special cases. This paper focuses on the design of efficient IPMs algorithm for CO problems based on kernel functions. After briefly introducing the main concepts of CO, we study some kernel functions, including the classical logarithmic barrier function, self-regular and also non self-regular functions. The iteration complexity obtained for CO is the same as the best bound for primal-dual interior point methods in LO.