An Interior-Point Approach to Sensitivity Analysis in Degenerate Linear Programs

An Interior-Point Approach to Sensitivity Analysis in Degenerate Linear Programs

We consider the interior-point approach to sensitivity analysis in linear programming developed by the authors. We investigate the quality of the interior-point bounds under degeneracy. In the case of a special degeneracy, we show that these bounds have the same nice asymptotic relationship with the optimal partition bounds as in the nondegenerate case. We prove a weaker relationship for genera...

Presolove Analysis of Linear Programs Prior to Applying an Interior Point Method

Several issues concerning an analysis of large and sparse linear programming problems prior to solving them with an interior point based optimizer are addressed in this paper. Three types of presolve procedures are distinguished. Routines from the rst class repeatedly analyze an LP problem formulation: eliminate empty or singleton rows and columns, look for primal and dual forcing or dominated ...

An interior point approach to postoptimal and parametric analysis in linear programming

In practice, understanding the behavior of the solution of the linear programming problem due to changes in the data is often as important as obtaining the optimal solution itself. Postoptimal analysis based on the simplex method by using an optimal basis is well established and widely used. However, in case of degenerate optimal solutions, due to nonunicity of optimal bases, problems arise in ...

An Interior-point Perspective on Sensitivity Analysis in Linear Programming and Semidefinite Programming

A general parametric analysis approach and its implication to sensitivity analysis in interior point methods

Adler and Monteiro (1992) developed a parametric analysis approach that is naturally related to the geometry of the linear pro~am. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, we develop an altemative geometric approach for parametric analysis which does not require the strong complementarity condition. This pa...