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|Title: ||Global Optimization with the DIRECT Algorithm|
|Authors: ||Finkel, Daniel Edwin|
|Advisors: ||C.T. Kelley, Committee Chair|
S. Ghosal, Committee Member
H. Tran, Committee Member
R. Smith, Committee Member
|Keywords: ||sampling methods|
|Issue Date: ||22-Feb-2005|
|Discipline: ||Operations Research|
|Abstract: ||This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for bound-constrained problems. We rigorously show that a sub-sequence of the points sampled by the algorithm satisfy first order necessary conditions for both smooth and non-smooth problems. We show linear convergence of the algorithm for linear problems, and demonstrate why our analysis cannot be extended to more general problems.
We analyze a parameter of DIRECT, and show that it negatively affects the performance of the algorithm. A modified version of the DIRECT is introduced. Test examples are used to demonstrate the effectiveness of the modified algorithm.
We apply DIRECT to six well-field optimization problems from the literature. We collect data on the problems with DIRECT, and utilize statistical methods to glean information from the data about the well-field problems.|
|Appears in Collections:||Dissertations|
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