Persistent Link:
http://hdl.handle.net/10150/195299
Title:
Study on Optimality Conditions in Stochastic Linear Programming
Author:
Zhao, Lei
Issue Date:
2005
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:
In the rapidly changing world of today, people have to make decisions under some degree of uncertainty. At the same time, the development of computing technologies enables people to take uncertain factors into considerations while making their decisions.Stochastic programming techniques have been widely applied in finance engineering, supply chain management, logistics, transportation, etc. Such applications often involve a large, possibly infinite, set of scenarios. Hence the resulting programstend to be large in scale.The need to solve large scale programs calls for a combination of mathematical programming techniques and sample-based approximation. When using sample-based approximations, it is important to determine the extent to which the resulting solutions are dependent on thespecific sample used. This dissertation research focuses on computational evaluation of the solutions from sample-based two-stage/multistage stochastic linear programming algorithms, with a focus on the effectiveness of optimality tests and the quality ofa proposed solution.In the first part of this dissertation, two alternative approaches of optimality tests of sample-based solutions, adaptive and non-adaptive sampling methods, are examined and computationally compared. The results of the computational experiment are in favor of the adaptive methods. In the second part of this dissertation, statistically motivated bound-based solution validation techniques in multistage linear stochastic programs are studied both theoretically and computationally. Different approaches of representations of the nonanticipativity constraints are studied. Bounds are established through manipulations of the nonanticipativity constraints.
Type:
text; Electronic Dissertation
Keywords:
stochastic linear programming; optimality conditions; solution validation; sample-based algorithms; statistically motivated bounds
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Systems & Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Higle, Julia L.
Committee Chair:
Higle, Julia L.

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleStudy on Optimality Conditions in Stochastic Linear Programmingen_US
dc.creatorZhao, Leien_US
dc.contributor.authorZhao, Leien_US
dc.date.issued2005en_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.abstractIn the rapidly changing world of today, people have to make decisions under some degree of uncertainty. At the same time, the development of computing technologies enables people to take uncertain factors into considerations while making their decisions.Stochastic programming techniques have been widely applied in finance engineering, supply chain management, logistics, transportation, etc. Such applications often involve a large, possibly infinite, set of scenarios. Hence the resulting programstend to be large in scale.The need to solve large scale programs calls for a combination of mathematical programming techniques and sample-based approximation. When using sample-based approximations, it is important to determine the extent to which the resulting solutions are dependent on thespecific sample used. This dissertation research focuses on computational evaluation of the solutions from sample-based two-stage/multistage stochastic linear programming algorithms, with a focus on the effectiveness of optimality tests and the quality ofa proposed solution.In the first part of this dissertation, two alternative approaches of optimality tests of sample-based solutions, adaptive and non-adaptive sampling methods, are examined and computationally compared. The results of the computational experiment are in favor of the adaptive methods. In the second part of this dissertation, statistically motivated bound-based solution validation techniques in multistage linear stochastic programs are studied both theoretically and computationally. Different approaches of representations of the nonanticipativity constraints are studied. Bounds are established through manipulations of the nonanticipativity constraints.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectstochastic linear programmingen_US
dc.subjectoptimality conditionsen_US
dc.subjectsolution validationen_US
dc.subjectsample-based algorithmsen_US
dc.subjectstatistically motivated boundsen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems & Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorHigle, Julia L.en_US
dc.contributor.chairHigle, Julia L.en_US
dc.contributor.committeememberHigle, Julia L.en_US
dc.contributor.committeememberSen, Suvrajeeten_US
dc.contributor.committeememberSmith, J. Coleen_US
dc.contributor.committeememberZeng, Danielen_US
dc.contributor.committeememberFenstermacher, Kurt D.en_US
dc.identifier.proquest1343en_US
dc.identifier.oclc137355145en_US
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