Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term

Abstract EN

We introduce a new parametric kernel function, which is a combination of the classic kernelfunction and a trigonometric barrier term, and present various properties of this new kernel function.

Aclass of large- and small-update primal-dual interior-point methods for linear optimization based on thisparametric kernel function is proposed.

By utilizing the feature of the parametric kernel function, we derivethe iteration bounds for large-update methods, O ( n 2 / 3 log ( n / ε ) ) , and small-update methods, O ( n log ( n / ε ) ) .

These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.