A structured reduced sequential quadratic programming and its application to a shape design problem

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dc.contributor.authorKang, Kyehongen
dc.contributor.committeechairHerdman, Terry L.en
dc.contributor.committeememberBurns, John A.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberGunzburger, Max D.en
dc.contributor.committeememberLin, Taoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:14:53Zen
dc.date.adate2006-06-07en
dc.date.available2014-03-14T21:14:53Zen
dc.date.issued1994-09-15en
dc.date.rdate2006-06-07en
dc.date.sdate2006-06-07en
dc.description.abstractThe objective of this work is to solve a model one dimensional duct design problem using a particular optimization method. The design problem is formulated as an equality constrained optimization, called All at once method, so that the analysis problem is not solved until the optimal design is reached. Furthermore, the block structure in the Jacobian of the linearized constraints is exploited by decomposing the variables into the design and flow parts. To achieve this, Sequential quadratic programming with BFGS update for the reduced Hessian of the Lagrangian function is used with Variable reduction method which preserves the structure of the Jacobian in representing the null space basis matrix. By updating the reduced Hessians only of which the dimension is the number of design variables, the storage requirement for Hessians is reduced by a large amount. In addition, the flow part of the Jacobian can be computed analytically. The algorithm with a line search globalization is described. A global and local analysis is provided with a modification of the paper by Byrd and Nocedal [Mathematical Programming 49(1991) pp 285-323] in which they analyzed the similar algorithm with the Orthogonal factorization method which assumes the orthogonality of the null space basis matrix. Numerical results are obtained and compared favorably with results from the Black box method - unconstrained optimization formulation.en
dc.description.degreePh. D.en
dc.format.extentviii, 85 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06072006-124216en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06072006-124216/en
dc.identifier.urihttp://hdl.handle.net/10919/38565en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1994.K364.pdfen
dc.relation.isformatofOCLC# 32807042en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1994.K364en
dc.subject.lcshQuadratic programmingen
dc.titleA structured reduced sequential quadratic programming and its application to a shape design problemen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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