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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
derivative-free optimization
global optimization
Issue Date: 22-Feb-2005
Degree: PhD
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.
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