Algorithms for Derivative-Free Optimization

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Industrial Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Rios, Luis Miguel

Contributors dc:contributor

• Nikolaos Sahinidis

• Operations Research

Language dc:language

eng

Identifier

(MiAaPQ)AAI3363076

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87095