Generalized support set invariancy sensitivity analysis in linear optimization

Abstract

Support set invariancy sensitivity analysis deals with finding the range of the parameter variation where there are optimal solutions with the same positive variables for all parameter values throughout this range. This approach to sensitivity analysis has been studied for Linear Optimization (LO) and Convex Quadratic Optimization (CQO) problems, when they are in standard form. In practice, most problems are in <em>general form</em>, in addition to nonnegative variables and equalities, they include free variables and inequalities. The LO problem in general form can be converted into the standard form, but this transforming changes the meaning of the support set invariancy sensitivity analysis. <br>&nbsp; &nbsp In this paper, we consider the primal and dual LO problems in general form and introduce the associated general standard form. It is shown that investigating support set invariancy sensitivity analysis for this general standard form is able to accommodate not only the support set invariancy sensitivity analysis for usual standard form, but also the classic study of sensitivity analysis based on simplex methods as well as the recent point of view of sensitivity analysis based on interior point methods.