Primal-Dual Interior-Point Methods for Second-Order
Conic Optimization Based on Self-Regular Proximities
Based on the notion of self-regularity associated with the second-order cone, this chapter deals with primal-dual Newton methods for solving SOCO problems. After a brief introduction to the problem under consideration, general analytical functions associated with the second-order cone are introduced and versatile properties of these functions are exploited. Special attention is paid to self-regular functions and self-regular proximities related to the second-order cone K. New search directions for large-update primal-dual IPMsfor solving the underlying problem are then proposed and the complexity results of the corresponding algorithms are presented.