Multiparametric linear programming: Support set and optimal partition invariancy

This paper reflects the renascence of sensitivity and parametric analysis in linear programming and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does. Interior point methods in linear optimization suppressed the traditional parametric analysis based on preserving optimal basis and gave rise to new ones. In this paper there is presented a description of the set of admissible parameters under so called support set invariancy and optimal partition invariancy and compared with the classical optimal basis concept. Such a description can be used e.g. for tolerance analysis.