Global Optimization in Least Squares Problems in FTIR Spectroscopy and X -Ray Crystallography

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemical and Biomolecular Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Vaia, Anastasia

Contributors dc:contributor

• Nikolaos Sahinidis

• Engineering, Chemical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3101985

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/82357