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.
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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Degirmenci, Soysal"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Electrical & Systems Engineering","degree_department":null,"school":null,"contributors":["Joseph A. O'Sullivan","David G. Politte, Arye Nehorai, Mark Anastasio, Jr-Shin Li,"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-05-15T07:00:00Z","date_published":"2016-05-15T07:00:00Z","updated_at":"2026-07-24T06:13:14Z","subjects":["computational imaging","convex optimization","jensen surrogates","machine learning","optimization","Applied Mathematics","Electrical and Electronics"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/eng_etds/157"],"render_values":[{"text":"https://openscholarship.wustl.edu/eng_etds/157","href":"https://openscholarship.wustl.edu/eng_etds/157","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/K7K35RXN","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Joseph A. O'Sullivan","David G. Politte, Arye Nehorai, Mark Anastasio, Jr-Shin Li,"]},{"key":"dc:creator","label":"Author","values":["Degirmenci, Soysal"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-15T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Systems Engineering","McKelvey School of Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["computational imaging","convex optimization","jensen surrogates","machine learning","optimization","Applied Mathematics","Electrical and Electronics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/K7K35RXN","https://openscholarship.wustl.edu/eng_etds/157"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Permanent URL: https://doi.org/10.7936/K7K35RXN"]},{"key":"dc:description.abstract","label":"Abstract","values":["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.
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.
"]},{"key":"dc:title","label":"Title","values":["A General Framework of Large-Scale Convex Optimization Using Jensen Surrogates and Acceleration Techniques"]}]}],"canonical_facts":{"dc:contributor":["Joseph A. O'Sullivan","David G. Politte, Arye Nehorai, Mark Anastasio, Jr-Shin Li,"],"dc:creator":["Degirmenci, Soysal"],"dc:date.available":["2016-05-15T07:00:00Z"],"dc:description":["Permanent URL: https://doi.org/10.7936/K7K35RXN"],"dc:description.abstract":["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.
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.
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