Abstract
In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.
Highlights
We focus on the primal problem of semidefinite optimization (SDO) in the standard form (P)
Kernel functions play an important role in the design and analysis of primal-dual (IPMs) for optimization and complementarity problems
We have investigated a class of large-update primal-dual (IPMs) for (LO) based on a parametric kernel function presented in [16] can be extended to the context of (SDO)
Summary
We focus on the primal problem of semidefinite optimization (SDO) in the standard form (P). Kernel functions play an important role in the design and analysis of primal-dual (IPMs) for optimization and complementarity problems. They are used for determining the search directions and for measuring the distance between the given iterate and the μ -center for the algorithms. The purpose of the paper is to extend the primal-dual large-update (IPMs) for (LO) based on the parametric function considered in [15] to (SDO) by using the NT-scaling scheme [11, 21].
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