A General Framework of Large-Scale Convex Optimization Using Jensen Surrogates and Acceleration Techniques

<p>In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.</p> <p>In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, we present non-asymptotic convergence analysis of this family of methods and the motivation behind developing accelerated variants. Moreover, we discuss widely used acceleration techniques for convex optimization and then investigate acceleration techniques that can be used within the Jensen surrogate framework while proposing several novel acceleration methods. Furthermore, we show that proposed methods perform competitively with or better than state-of-the-art algorithms for several applications including Sparse Linear Regression (Image Deblurring), Positron Emission Tomography, X-Ray Transmission Tomography, Logistic Regression, Sparse Logistic Regression and Automatic Relevance Determination for X-Ray Transmission Tomography.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Systems Engineering

Year dc:date.available

2016

Author dc:creator

• Degirmenci, Soysal

Contributors dc:contributor

• Joseph A. O'Sullivan
• David G. Politte, Arye Nehorai, Mark Anastasio, Jr-Shin Li,

• computational imaging
• convex optimization
• jensen surrogates
• machine learning
• optimization
• Applied Mathematics
• Electrical and Electronics

Statement dc:rights

• I have not registered my thesis with the U.S. Copyright Office, and do not intend to.

Language dc:language

English (en)

Identifier

https://openscholarship.wustl.edu/eng_etds/157

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:eng_etds-1157