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Subgradient Optimization Methods in Integer Programming with an Application to a Radiation Therapy Problem

  • The thesis deals with the subgradient optimization methods which are serving to solve nonsmooth optimization problems. We are particularly concerned with solving large-scale integer programming problems using the methodology of Lagrangian relaxation and dualization. The goal is to employ the subgradient optimization techniques to solve large-scale optimization problems that originated from radiation therapy planning problem. In the thesis, different kinds of zigzagging phenomena which hamper the speed of the subgradient procedures have been investigated and identified. Moreover, we have established a new procedure which can completely eliminate the zigzagging phenomena of subgradient methods. Procedures used to construct both primal and dual solutions within the subgradient schemes have been also described. We applied the subgradient optimization methods to solve the problem of minimizing total treatment time of radiation therapy. The problem is NP-hard and thus far there exists no method for solving the problem to optimality. We present a new, efficient, and fast algorithm which combines exact and heuristic procedures to solve the problem.

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Author:Berhanu Guta
URN (permanent link):urn:nbn:de:bsz:386-kluedo-16224
Advisor:Horst W. Hamacher
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2003
Year of Publication:2003
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2003/09/17
Date of the Publication (Server):2003/09/26
Tag:Lagrangian relaxation; integer programming; multileaf collimator; radiation therapy; subgradient
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011