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

Adler and Monteiro developed a parametric analysis approach that is naturally related to the geometry of the linear program. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, the authors develop an alternative geometric approach for parametric analysis which does not require the strong complementarity condition. This parametric analysis approach is used to develop range and marginal analysis techniques which are suitable for interior point methods. Two approaches are developed, namely the LU factorization approach and the affine scaling approach.