Tapia, Richard A.2009-06-042009-06-041991El-Bakry, Amr Saad Mohamed. "On the role of indicators in identifying zero variables in linear programming." (1991) Diss., Rice University. <a href="https://hdl.handle.net/1911/16436">https://hdl.handle.net/1911/16436</a>.https://hdl.handle.net/1911/16436In this research we study the role of indicator functions in the identification and the removal of zero variables in linear programming. The definition and desired properties of the indicators are given. We investigate the behavior of the Tapia and the primal-dual indicators in the framework of the recently proposed primal-dual interior-point methods. The structure of the solution set of the linear programming problem is closely examined. We prove the interesting result that the relative interior of the solution set coincides with the set of solutions that satisfy strict complementarity. The implications of this result in the context of several indicators is studied. A procedure to identify and remove zero variables is proposed. Finally, we present numerical experiments that demonstrate the use of that procedure in saving computational work and improving the performance of the primal-dual interior-point methods.77 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH. 1991 EL-BAKRY