In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.
","abstract_html":"<p>In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.</p>","abstract_has_math":false,"creators":["Thomas, William Howard, II"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["John J. Swetits","Wu Li","Hideaki Kaneko","Przemek Bogacki"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-07-01T07:00:00Z","date_published":"2007-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:00Z","subjects":["Convex quadratic splines","Quasi-Newton methods","Splines","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines"]}]}],"canonical_facts":{"dc:contributor":["John J. Swetits","Wu Li","Hideaki Kaneko","Przemek Bogacki"],"dc:creator":["Thomas, William Howard, II"],"dc:date.available":["2019-06-13T07:00:00Z"],"dc:description.abstract":["In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.
"],"dc:identifier":["9780549218265","https://digitalcommons.odu.edu/mathstat_etds/64"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Convex quadratic splines","Quasi-Newton methods","Splines","Mathematics"],"dc:title":["On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:00Z"}