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

A dissertation submitted to the Faculty of Science School of Computational and Applied Mathematics, University of the Witwatersrand,

Johannesburg. April 27, 2013. / In 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.

Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12914 |

Date | 29 July 2013 |

Creators | Newby, Eric |

Source Sets | South African National ETD Portal |

Language | English |

Detected Language | English |

Type | Thesis |

Format | application/pdf |

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