{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/19195"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/19195","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming","abstract":"Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the perturbed Karush-Kuhn-Tucker condition and primarily forces feasibility in the constraints. In order to globalize the method using a linesearch strategy, a modified augmented Lagrangian merit function is defined in terms of the centrality condition. The second class is the Quasi-Newton interior-point methods. In this class the well known Boggs-Tolle-Wang characterization of Q-superlinear convergence for Quasi-Newton method for equality constrained optimization is extended. Critical issues in this extension are; the choice of the centering parameter, the choice of the steplength parameter, and the choice of the primary variables.","abstract_html":"Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the perturbed Karush-Kuhn-Tucker condition and primarily forces feasibility in the constraints. In order to globalize the method using a linesearch strategy, a modified augmented Lagrangian merit function is defined in terms of the centrality condition. The second class is the Quasi-Newton interior-point methods. In this class the well known Boggs-Tolle-Wang characterization of Q-superlinear convergence for Quasi-Newton method for equality constrained optimization is extended. Critical issues in this extension are; the choice of the centering parameter, the choice of the steplength parameter, and the choice of the primary variables.","abstract_has_math":false,"creators":["Paroda Garcia, Zeferino"],"institution":"Rice University","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Engineering","degree_department":null,"school":null,"contributors":[],"advisors":["Tapia, Richard A."],"committee_chairs":[],"committee_members":[],"year":1997,"date_issued":"1997","date_published":"1997","updated_at":"2026-07-24T04:10:32Z","subjects":["Mathematics","Operations research","Computer science"],"languages":["eng"],"rights":["Copyright 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."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/19195","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Tapia, Richard A."]},{"key":"dc:creator","label":"Author","values":["Paroda Garcia, Zeferino"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2009-06-04T07:55:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-06-04T07:55:42Z"]},{"key":"dc:date.issued","label":"Date","values":["1997"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Operations research","Computer science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1911/19195"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the perturbed Karush-Kuhn-Tucker condition and primarily forces feasibility in the constraints. In order to globalize the method using a linesearch strategy, a modified augmented Lagrangian merit function is defined in terms of the centrality condition. The second class is the Quasi-Newton interior-point methods. In this class the well known Boggs-Tolle-Wang characterization of Q-superlinear convergence for Quasi-Newton method for equality constrained optimization is extended. Critical issues in this extension are; the choice of the centering parameter, the choice of the steplength parameter, and the choice of the primary variables."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming"]}]}],"canonical_facts":{"dc:contributor.advisor":["Tapia, Richard A."],"dc:creator":["Paroda Garcia, Zeferino"],"dc:date.accessioned":["2009-06-04T07:55:42Z"],"dc:date.available":["2009-06-04T07:55:42Z"],"dc:date.issued":["1997"],"dc:description.abstract":["Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the perturbed Karush-Kuhn-Tucker condition and primarily forces feasibility in the constraints. In order to globalize the method using a linesearch strategy, a modified augmented Lagrangian merit function is defined in terms of the centrality condition. The second class is the Quasi-Newton interior-point methods. In this class the well known Boggs-Tolle-Wang characterization of Q-superlinear convergence for Quasi-Newton method for equality constrained optimization is extended. Critical issues in this extension are; the choice of the centering parameter, the choice of the steplength parameter, and the choice of the primary variables."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1911/19195"],"dc:language.iso":["eng"],"dc:rights":["Copyright 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."],"dc:subject":["Mathematics","Operations research","Computer science"],"dc:title":["A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:32Z"}