Persistent Link:
http://hdl.handle.net/10150/186701
Title:
EXTRAPOLATED LEAST SQUARES OPTIMIZATION APPLIED TO LENS DESIGN.
Author:
HUBER, EDWARD DAVID.
Issue Date:
1982
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:
A new approach to least squares optimization has been developed which uses extrapolation factors to introduce variable metric techniques into the least squares optimization methods used in optical design. This new approach retains derivative information between successive optimization iterative steps to form approximate second derivatives in order to develop extrapolation factors. These extrapolation factors are used to update and refine important system parameters including the merit function, the first derivative matrix and the system metric without requiring the reevaluation of the system derivatives. This extrapolated least squares (ELS) optimization method does not simply add damping terms to the diagonal elements of the system metric to control optimization step lengths as is done in the various damped least squares (DLS) optimization methods; but the total system metric is updated to reflect the current optimization progress made to within the limit of the extrapolated quadratic approximation to the problem. The ELS and conventional least squares optimization methods are compared in numerous optimization problem examples including several test functions as well as typical optical design problems. The extrapolated least squares (ELS) optimization method is shown to reduce computational overhead and to accelerate convergence of least squares types of optimization problems.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Optical Sciences; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Shannon, Robert R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleEXTRAPOLATED LEAST SQUARES OPTIMIZATION APPLIED TO LENS DESIGN.en_US
dc.creatorHUBER, EDWARD DAVID.en_US
dc.contributor.authorHUBER, EDWARD DAVID.en_US
dc.date.issued1982en_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.abstractA new approach to least squares optimization has been developed which uses extrapolation factors to introduce variable metric techniques into the least squares optimization methods used in optical design. This new approach retains derivative information between successive optimization iterative steps to form approximate second derivatives in order to develop extrapolation factors. These extrapolation factors are used to update and refine important system parameters including the merit function, the first derivative matrix and the system metric without requiring the reevaluation of the system derivatives. This extrapolated least squares (ELS) optimization method does not simply add damping terms to the diagonal elements of the system metric to control optimization step lengths as is done in the various damped least squares (DLS) optimization methods; but the total system metric is updated to reflect the current optimization progress made to within the limit of the extrapolated quadratic approximation to the problem. The ELS and conventional least squares optimization methods are compared in numerous optimization problem examples including several test functions as well as typical optical design problems. The extrapolated least squares (ELS) optimization method is shown to reduce computational overhead and to accelerate convergence of least squares types of optimization problems.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineOptical Sciencesen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorShannon, Robert R.en_US
dc.identifier.proquest8217423en_US
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