Generalized Support Set Invariancy Sensitivity Analysis

Alireza Ghaffari Hadigheh (hadighehaoptlab.mcmaster.ca)
Tamas Terlaky (terlakymcmaster.ca)

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 \emph{general form}, in addition to nonnegative variables and equalities, they include free variables and inequalities. Though, 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. In this paper, we consider the primal and dual LO problems in general form and investigate support set invariancy sensitivity analysis for them. We present computable LO problems to identify the associated support set invariancy intervals for LO problem and investigate their relationship to support set invariancy intervals for LO problem in standard form.

Keywords: Parametric optimization, sensitivity analysis, linear optimization, interior point method, optimal partition, support set invariancy, active constraint set

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Sunbitted to the Journal of industrial and management optimization

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Entry Submitted: 07/05/2005
Entry Accepted: 07/05/2005
Entry Last Modified: 07/05/2005

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