THE COMPUTATIONAL ASPECTS OF POSTOPTIMAL ANALYSIS OF GEOMETRIC PROGRAMS

Persistent Link:
http://hdl.handle.net/10150/282013
Title:
THE COMPUTATIONAL ASPECTS OF POSTOPTIMAL ANALYSIS OF GEOMETRIC PROGRAMS
Author:
Stiglich, George Randall
Issue Date:
1981
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Optimal engineering design specifications are usually derived from an iterative design process. Here, different mathematical programs, each representing a particular problem assumption, are solved in order to gain insight into how and why an ideal design changes as model parameters vary. The mathematical technique used in this process is termed sensitivity analysis. The focus of this study is on techniques for performing such analysis on optimization problems which can be modeled as geometric programs. A dual based computationally attractive numerical procedure was developed to generate the locus of optimal solutions to prototype geometric programs corresponding to a large set of program parameter trajectories. Coefficient variation can include individual or simultaneous changes in any or all cost and exponent values. Sensitivity analysis is accomplished by numerically solving a specially constructed nonlinear initial value differential equation problem. Computational procedures were developed for computing an intitial value point, differential equation construction and solution, primal/dual conversion and problem reconstruction in the event of a primal constraint status change. A computer program written to carry out this scheme was described and used in the design of a batch process chemical plant. Preliminary results show the sensitivity analysis procedure developed in this study is attractive in terms of required computation time and perturbation flexibility of model coefficients.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Geometric programming.; Differential equations -- Numerical solutions -- Computer programs.; Engineering design.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Systems and Industrial Engineering
Degree Grantor:
University of Arizona
Advisor:
Trzeciak, John

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleTHE COMPUTATIONAL ASPECTS OF POSTOPTIMAL ANALYSIS OF GEOMETRIC PROGRAMSen_US
dc.creatorStiglich, George Randallen_US
dc.contributor.authorStiglich, George Randallen_US
dc.date.issued1981en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractOptimal engineering design specifications are usually derived from an iterative design process. Here, different mathematical programs, each representing a particular problem assumption, are solved in order to gain insight into how and why an ideal design changes as model parameters vary. The mathematical technique used in this process is termed sensitivity analysis. The focus of this study is on techniques for performing such analysis on optimization problems which can be modeled as geometric programs. A dual based computationally attractive numerical procedure was developed to generate the locus of optimal solutions to prototype geometric programs corresponding to a large set of program parameter trajectories. Coefficient variation can include individual or simultaneous changes in any or all cost and exponent values. Sensitivity analysis is accomplished by numerically solving a specially constructed nonlinear initial value differential equation problem. Computational procedures were developed for computing an intitial value point, differential equation construction and solution, primal/dual conversion and problem reconstruction in the event of a primal constraint status change. A computer program written to carry out this scheme was described and used in the design of a batch process chemical plant. Preliminary results show the sensitivity analysis procedure developed in this study is attractive in terms of required computation time and perturbation flexibility of model coefficients.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectGeometric programming.en_US
dc.subjectDifferential equations -- Numerical solutions -- Computer programs.en_US
dc.subjectEngineering design.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorTrzeciak, Johnen_US
dc.identifier.proquest8126182en_US
dc.identifier.oclc8706890en_US
dc.identifier.bibrecord.b13912884en_US
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