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

We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, O(n2/3log⁡(n/ε)), and small-update methods, O(nlog⁡(n/ε)). These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions

Kernel-function Based Primal-Dual Algorithms for

Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigated a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper

Generic primal-dual interior point methods based on a new kernel function

In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed inSoftware TechnologyElectrical Engineering, Mathematics and Computer Scienc