Role of New Kernel Function in Complexity Analysis of an Interior Point Algorithm for Semi definite Linear Complementarity Problem

TL;DR

This paper introduces a novel kernel function for primal-dual interior point algorithms in semidefinite linear complementarity problems, simplifying analysis and improving computational efficiency.

Contribution

The paper presents a new kernel function that enhances the design and analysis of interior point methods for semidefinite problems, leading to better complexity bounds.

Findings

Improved complexity analysis for interior point algorithms.

Significant reduction in computation time and iterations.

Demonstrated practical performance improvements in numerical tests.

Abstract

In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its properties, allow us a great simplicity for the analysis of interior-point method, therefore the complexity of large-update primal-dual interior point is the best so far. Numerical tests have shown that the use of this function gave a big improvement in the results concerning the time and the number of iterations. so is well promising and perform well enough in practice in comparison with some other existing results in the literature.