General solution methods for mixed integer quadratic programming and derivative free mixed integer non-linear programming problems

Simple item page
dc.contributor.authorNewby, Eric
dc.date.accessioned2013-07-29T12:30:03Z
dc.date.available2013-07-29T12:30:03Z
dc.date.issued2013-07-29
dc.descriptionA dissertation submitted to the Faculty of Science School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg. April 27, 2013.en_ZA
dc.description.abstractIn a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of convergence to local minima are provided for two of the implementations. In the development of the algorithm several other contributions are made. The derivative free algorithm requires the solution of several mixed integer quadratic programming subproblems and novel methods for solving nonconvex instances of these problems are developed in this thesis. Additionally, it is shown that the current definitions of local minima for mixed integer programs are deficient and a rigorous approach to developing possible definitions is proposed. Using this approach we propose a new definition which improves on those currently used in the literature. Other components of this thesis are an overview of derivative based mixed integer non-linear programming, extensive reviews of mixed integer quadratic programming and deterministic derivative free optimization and extensive computational results illustrating the effectiveness of the contributions mentioned in the previous paragraphs.en_ZA
dc.identifier.urihttp://hdl.handle.net/10539/12914
dc.language.isoenen_ZA
dc.subject.lcshInteger programming.
dc.subject.lcshNonlinear programming.
dc.subject.lcshProgramming (Mathematics)
dc.titleGeneral solution methods for mixed integer quadratic programming and derivative free mixed integer non-linear programming problemsen_ZA
dc.typeThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
PhD_E-Newby_0705761J.pdf
Size:
1.64 MB
Format:
Adobe Portable Document Format
Description:
Main article
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
ETD Collection