Enhancing the behavior of interior-point methods via identification of variables

Authors:
María D. González-Lima
Affiliations:
Departamento de Cómputo Científico y Estadística y Centro de Estadística y Software Matemático (CESMa), Universidad Simón Bolívar, Caracas, Venezuela
Venue:
Optimization Methods & Software
Year:
2007

Citing 8
Cited 0

A primal-dual interior point algorithm for linear programming

Progress in Mathematical Programming Interior-point and related methods
Pathways to the optimal set in linear programming

Progress in Mathematical Programming Interior-point and related methods
A study of indicators for identifying zero variables in interior-point methods

SIAM Review
Solving nonlinear multicommodity flow problems by the analytic center cutting plane method

Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Primal-dual interior-point methods

Primal-dual interior-point methods
Primal—dual—infeasible Newton approach for the analytic center deep-cutting plane method

Journal of Optimization Theory and Applications
On Effectively Computing the Analytic Center of the Solution Set by Primal-Dual Interior-Point Methods

SIAM Journal on Optimization
Preconditioning Indefinite Systems in Interior Point Methods for Optimization

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In many linear programming models of real life problems the solution set is not bounded. The presence of unbounded variables in the solution set can severely hurt the practical performance of primal-dual interior-point methods for linear programming that generate iterates which follow closely the central path or converge to the analytic center. In this work we study the effect of the unbounded variables by analysing the numerical behavior of the LSSN algorithm proposed by González-Lima, Tapia and Potra 1. when applied to linear problems with unbounded solution sets. We discuss the numerical behavior of the algorithm and we present a numerical procedure, based on the performance of the algorithm, to identify and remove the unbounded variables and related constraints. We develop theoretical support for the procedure and experimental evidence of its performance.