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https://hdl.handle.net/2142/87095
Description
Title
Algorithms for Derivative-Free Optimization
Author(s)
Rios, Luis Miguel
Issue Date
2009
Doctoral Committee Chair(s)
Nikolaos Sahinidis
Department of Study
Industrial Engineering
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Operations Research
Language
eng
Abstract
In this thesis, we begin by presenting a comprehensive list of available methods and software and performing an extensive computational study that compares the solvers over a publicly available problem set. Then, we develop Model and Search (M&S), a new local search algorithm for derivative-free optimization. M&S performs a local search from a given point. The search is guided by identifying descent directions from a quadratic model fitted around the best known point, while using information from other evaluated points. We prove that M&S enjoys global convergence to a stationary point. We also propose a new global search algorithm for derivative-free optimization problems, in particular the Branch and Model (B&M) algorithm that is based on modeling the function of interest around each evaluated point by using information from other nearby evaluated points. Algorithm B&M is shown to perform a dense search and thus converge to a global minimum. While oriented towards a global search, B&M relies on the M&S algorithm for occasional local searches. Finally, we present an application of derivative-free solvers, including B&M, to the protein-ligand docking problem. Results show that B&M delivers satisfactory ligand conformations, even outperforming the state-of-the-art protein docking software AutoDock.
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