Persistent Link:
http://hdl.handle.net/10150/185857
Title:
Inexact subgradient methods.
Author:
Au, Kelly Thurston.
Issue Date:
1992
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 solving a mathematical program, the exact evaluation of the objective function and its subgradients can be computationally burdensome. For example, in a stochastic program, the objective function is typically defined through a multi-dimensional integration. Solution procedures for stochastic programs are usually based on functional approximation techniques, or statistical applications of subgradient methods. In this dissertation, we explore algorithms by combining functional approximation techniques with subgradient optimization methods. This class of algorithms is referred to as "inexact subgradient methods". First, we develop a basic inexact subgradient method and identify conditions under which this approach will lead to an optimal solution. We also offer an inexact subgradient algorithm by adaptively defining the steplengths via estimated bounds on the deviations from optimality. Second, we explore approaches in which functional approximation techniques can be combined with a primal-dual subgradient method. In these algorithms, the steplengths are defined via the primal and dual information. Hence suggestions to optimality can be reflected through the steplengths, as the iteration proceeds. We also incorporate space dilation operations, which stabilize the moving directions, within our basic inexact subgradient method. As an example of the applicability of these methods, we use statistically defined approximations, which are similar to those derived in Stochastic Decomposition, in some of our algorithms for the solutions of stochastic programs.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Mathematics.; Subgradient methods.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Sen, Suvrajeet; Higle, Julia L.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleInexact subgradient methods.en_US
dc.creatorAu, Kelly Thurston.en_US
dc.contributor.authorAu, Kelly Thurston.en_US
dc.date.issued1992en_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 solving a mathematical program, the exact evaluation of the objective function and its subgradients can be computationally burdensome. For example, in a stochastic program, the objective function is typically defined through a multi-dimensional integration. Solution procedures for stochastic programs are usually based on functional approximation techniques, or statistical applications of subgradient methods. In this dissertation, we explore algorithms by combining functional approximation techniques with subgradient optimization methods. This class of algorithms is referred to as "inexact subgradient methods". First, we develop a basic inexact subgradient method and identify conditions under which this approach will lead to an optimal solution. We also offer an inexact subgradient algorithm by adaptively defining the steplengths via estimated bounds on the deviations from optimality. Second, we explore approaches in which functional approximation techniques can be combined with a primal-dual subgradient method. In these algorithms, the steplengths are defined via the primal and dual information. Hence suggestions to optimality can be reflected through the steplengths, as the iteration proceeds. We also incorporate space dilation operations, which stabilize the moving directions, within our basic inexact subgradient method. As an example of the applicability of these methods, we use statistically defined approximations, which are similar to those derived in Stochastic Decomposition, in some of our algorithms for the solutions of stochastic programs.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectMathematics.en_US
dc.subjectSubgradient methods.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSen, Suvrajeeten_US
dc.contributor.advisorHigle, Julia L.-
dc.contributor.committeememberSzidarovszky, Ferencen_US
dc.identifier.proquest9229852en_US
dc.identifier.oclc712675052en_US
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