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dc.contributor.authorDesai, Jitamitraen
dc.date.accessioned2014-03-14T20:13:45Zen
dc.date.available2014-03-14T20:13:45Zen
dc.date.issued2005-06-28en
dc.identifier.otheretd-07052005-124337en
dc.identifier.urihttp://hdl.handle.net/10919/28211en
dc.description.abstractEver since the advent of the simplex algorithm, linear programming (LP) has been extensively used with great success in many diverse fields. The field of discrete optimization came to the forefront as a result of the impressive developments in the area of linear programming. Although discrete optimization problems can be viewed as belonging to the class of nonconvex programs, it has only been in recent times that optimization research has confronted the more formidable class of continuous nonconvex optimization problems, where the objective function and constraints are often highly nonlinear and nonconvex functions, defined in terms of continuous (and bounded) decision variables. Typical classes of such problems involve polynomial, or more general factorable functions. This dissertation focuses on employing the Reformulation-Linearization Technique (RLT) to enhance model formulations and to design effective solution techniques for solving several practical instances of continuous nonconvex optimization problems, namely, the hard and fuzzy clustering problems, risk management problems, and problems arising in control systems. Under the umbrella of the broad RLT framework, the contributions of this dissertation focus on developing models and algorithms along with related theoretical and computational results pertaining to three specific application domains. In the basic construct, through appropriate surrogation schemes and variable substitution strategies, we derive strong polyhedral approximations for the polynomial functional terms in the problem, and then rely on the demonstrated (robust) ability of the RLT for determining global optimal solutions for polynomial programming problems. The convergence of the proposed branch-and-bound algorithm follows from the tailored branching strategy coupled with consistency and exhaustive properties of the enumeration tree. First, we prescribe an RLT-based framework geared towards solving the hard and fuzzy clustering problems. In the second endeavor, we examine two risk management problems, providing novel models and algorithms. Finally, in the third part, we provide a detailed discussion on studying stability margins for control systems using polynomial programming models along with specialized solution techniques.en
dc.publisherVirginia Techen
dc.relation.haspartDesai_Dissertation.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectglobal optimizationen
dc.subjectRLTen
dc.subjectfactorable programsen
dc.subjecthard and fuzzy clusteringen
dc.subjectrisk managementen
dc.subjectcontrol systemsen
dc.subjectnonconvex programsen
dc.subjectevent treesen
dc.titleSolving Factorable Programs with Applications to Cluster Analysis, Risk Management, and Control Systems Designen
dc.typeDissertationen
dc.contributor.departmentIndustrial and Systems Engineeringen
dc.description.degreePh. D.en
thesis.degree.namePh. D.en
thesis.degree.leveldoctoralen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineIndustrial and Systems Engineeringen
dc.contributor.committeechairSherali, Hanif D.en
dc.contributor.committeememberKoelling, C. Patricken
dc.contributor.committeememberFraticelli, Barbara M. P.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberSarin, Subhash C.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07052005-124337/en
dc.date.sdate2005-07-05en
dc.date.rdate2007-07-20en
dc.date.adate2005-07-20en


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