A polynomial-time algorithm for linear optimization based on a new class of kernel functions

Authors:
M. El Ghami;I. Ivanov;J. B. M. Melissen;C. Roos;T. Steihaug
Affiliations:
University of Bergen, Department of Informatics, Høyteknologisenteret, N-5020, Bergen, Norway;Delft University of Technology, Department of Information Systems and Algorithms, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Department of Information Systems and Algorithms, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Department of Information Systems and Algorithms, P.O. Box 5031, 2600 GA Delft, The Netherlands;University of Bergen, Department of Informatics, Høyteknologisenteret, N-5020, Bergen, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 8
Cited 5

Pathways to the optimal set in linear programming

on Progress in Mathematical Programming: Interior-Point and Related Methods
Interior path following primal-dual algorithms. Part I: Linear programming

Mathematical Programming: Series A and B
Path-following methods for linear programming

SIAM Review
Primal-dual interior-point methods

Primal-dual interior-point methods
Interior point algorithms: theory and analysis

Interior point algorithms: theory and analysis
A New Efficient Large-Update Primal-Dual Interior-Point Method Based on a Finite Barrier

SIAM Journal on Optimization
A new polynomial-time algorithm for linear programming

STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A Comparative Study of Kernel Functions for Primal-Dual Interior-Point Algorithms in Linear Optimization

SIAM Journal on Optimization

A Class of New Large-Update Primal-Dual Interior-Point Algorithms for $\emph{P}_\ast(\kappa)$ Linear Complementarity Problems

ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Polynomial interior-point algorithms for P*(K) horizontal linear complementarity problem

Journal of Computational and Applied Mathematics
A new kind of simple kennel function yielding good iteration bounds for primal-dual interior-point methods

Journal of Computational and Applied Mathematics
Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

Journal of Computational and Applied Mathematics
Complexity analysis and numerical implementation of primal-dual interior-point methods for convex quadratic optimization based on a finite barrier

Numerical Algorithms

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai, M.El Ghami and C. Roos [Y.Q. Bai, M. El Ghami, and C. Roos. A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (3) (2003) 766-782]. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such a class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. In order to achieve these complexity results, several new arguments had to be used for the analysis. The iteration bound of large-update interior-point methods based on these functions and analyzed in this paper, is shown to be O(nlognlogn@e). For small-update interior-point methods the iteration bound is O(nlogn@e), which is currently the best-known bound for primal-dual IPMs. We also present some numerical results which show that by using a new kernel function, the best iteration numbers were achieved in most of the test problems.