Global Optimization in Least Squares Problems in FTIR Spectroscopy and X -Ray Crystallography
Vaia, Anastasia
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https://hdl.handle.net/2142/82357
Description
Title
Global Optimization in Least Squares Problems in FTIR Spectroscopy and X -Ray Crystallography
Author(s)
Vaia, Anastasia
Issue Date
2003
Doctoral Committee Chair(s)
Nikolaos Sahinidis
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical and Biomolecular Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
"Finally, the last part of the thesis considers the ""phase problem"" in X-ray crystallography. In particular, we address the problem of estimating the three-dimensional atomic positions of crystal structures from diffraction measurements alone. Starting from the ""minimal principle"" model, we develop novel optimization formulations and algorithms that exploit the special model structure of the problem. For the case of centrosymmetric structures, we first formulate the problem as a 0--1 linear programming problem and suggest a branch-and-bound algorithm for solving it. Based on empirical observations regarding the nature of the solutions of this model, we then propose to solve it through a system of linear equations for which we develop a fast Gaussian elimination algorithm. For noncentrosymmetric structures, we reduce the phase problem to a mixed-integer quadratic problem and utilize a branch-and-bound algorithm for its solution."
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