Effective finite termination procedures in interior-point methods for linear programming

Simple item page
dc.contributor.advisorTapia, Richard A.en_US
dc.contributor.advisorEl-Bakry, Amr S.en_US
dc.creatorWilliams, Pamela Joyen_US
dc.date.accessioned2009-06-04T08:08:48Zen_US
dc.date.available2009-06-04T08:08:48Zen_US
dc.date.issued1998en_US
dc.description.abstractDue to the structure of the solution set, an exact solution to a linear program cannot be computed by an interior-point algorithm without adding features, such as finite termination procedures, to the algorithm. Finite termination procedures attempt to compute an exact solution in a finite number of steps. The addition of a finite termination procedure enables interior-point algorithms to generate highly accurate solutions for problems in which the ill-conditioning of the Jacobian in the neighborhood of the solution currently precludes such accuracy. The main ingredients of finite termination are activating the procedure, predicting the optimal partition, formulating a simple mathematical model to compute a solution and developing computational techniques to solve the model. Each of these issues are studied in turn in this thesis. First, the current optimal face identification models are extended to bounded variable linear programming problems. Distance to the lower and upper bounds are incorporated into the model to prevent the computed solution from violating the bound constraints. Theory in the literature is extended to the new model. Empirical evidence shows that the proposed model reduces the number of projection attempts needed to find an exact solution. When early termination is the goal, projection from a pure composite Newton step is advocated. However, the cost may exceed the benefits due to the average need of more than one projection attempt to find an exact solution. Variants of Mehrotra's predictor-corrector primal-dual interior-point algorithm provide the foundation for most practical interior-point codes. To take advantage of all available algorithmic information, we investigate the behavior of the Tapia predictor-corrector indicator, which incorporates the corrector step, to identify the optimal partition. Globally, the Tapia predictor-corrector indicator behaves poorly as do all indicators, but locally exhibits fast convergence.en_US
dc.format.extent103 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 1998 WILLIAMSen_US
dc.identifier.citationWilliams, Pamela Joy. "Effective finite termination procedures in interior-point methods for linear programming." (1998) Diss., Rice University. <a href="https://hdl.handle.net/1911/19328">https://hdl.handle.net/1911/19328</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19328en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectMathematicsen_US
dc.subjectOperations researchen_US
dc.titleEffective finite termination procedures in interior-point methods for linear programmingen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
9827461.PDF
Size:
3.07 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations