In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity of the new point after the feasibility step is guaranteed with a more strict upper bound. Another advantage of this method is that it uses full-Newton steps, which means that no calculation of the step size is required at each iteration and that the cost is decreased. The implementation and numerical results demonstrate the reliability of the method.
","abstract_html":"<p>In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity of the new point after the feasibility step is guaranteed with a more strict upper bound. Another advantage of this method is that it uses full-Newton steps, which means that no calculation of the step size is required at each iteration and that the cost is decreased. The implementation and numerical results demonstrate the reliability of the method.</p>","abstract_has_math":false,"creators":["Ozen, Mustafa"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Scott Kersey","Yan Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:22Z","subjects":["ETD","Linear complementarity problem","Interior-point method","Infeasible interior-point method","Full Newton-step","Applied Mathematics","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1296","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Scott Kersey","Yan Wu"]},{"key":"dc:creator","label":"Author","values":["Ozen, Mustafa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-20T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Linear complementarity problem","Interior-point method","Infeasible interior-point method","Full Newton-step","Applied Mathematics","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1296"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity of the new point after the feasibility step is guaranteed with a more strict upper bound. Another advantage of this method is that it uses full-Newton steps, which means that no calculation of the step size is required at each iteration and that the cost is decreased. The implementation and numerical results demonstrate the reliability of the method.
"]},{"key":"dc:title","label":"Title","values":["Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems"]}]}],"canonical_facts":{"dc:contributor":["Scott Kersey","Yan Wu"],"dc:creator":["Ozen, Mustafa"],"dc:date.available":["2015-06-20T07:00:00Z"],"dc:description.abstract":["In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity of the new point after the feasibility step is guaranteed with a more strict upper bound. Another advantage of this method is that it uses full-Newton steps, which means that no calculation of the step size is required at each iteration and that the cost is decreased. The implementation and numerical results demonstrate the reliability of the method.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1296"],"dc:subject":["ETD","Linear complementarity problem","Interior-point method","Infeasible interior-point method","Full Newton-step","Applied Mathematics","Other Mathematics"],"dc:title":["Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:22Z"}