Physical Sciences and Mathematics Commons^™

Addressing The Challenged Of Dcop Based Decision-Making Algorithms In Modern Power Systems, Luis Daniel Ramirez Burgueno

Open Access Theses & Dissertations

Natural disasters have been determined as the leading cause of power outages, causing not only huge economic losses, but also the interruption of crucial welfare activities and the arise of security concerns. Because of the later, decision-making considering grid modernization, power system economics, and system resiliency has been a crucial theme in power systemsâ?? research. The need to better withstand catastrophic events and reducing the dependency of bulky generating units has propelled the development and better management of behind-the-meter generation or distributed energy resources (DERs). DERs can assist in the grid in different manners, not only by meeting energy demand …

Model-Based Deep Learning For Computational Imaging, Xiaojian Xu

McKelvey School of Engineering Theses & Dissertations

This dissertation addresses model-based deep learning for computational imaging. The motivation of our work is driven by the increasing interests in the combination of imaging model, which provides data-consistency guarantees to the observed measurements, and deep learning, which provides advanced prior modeling driven by data. Following this idea, we develop multiple algorithms by integrating the classical model-based optimization and modern deep learning to enable efficient and reliable imaging. We demonstrate the performance of our algorithms by validating their performance on various imaging applications and providing rigorous theoretical analysis.

The dissertation evaluates and extends three general frameworks, plug-and-play priors (PnP), regularized …

Continuous-Time And Complex Growth Transforms For Analog Computing And Optimization, Oindrila Chatterjee

McKelvey School of Engineering Theses & Dissertations

Analog computing is a promising and practical candidate for solving complex computational problems involving algebraic and differential equations. At the fundamental level, an analog computing framework can be viewed as a dynamical system that evolves following fundamental physical principles, like energy minimization, to solve a computing task. Additionally, conservation laws, such as conservation of charge, energy, or mass, provide a natural way to couple and constrain spatially separated variables. Taking a cue from these observations, in this dissertation, I have explored a novel dynamical system-based computing framework that exploits naturally occurring analog conservation constraints to solve a variety of optimization …

Machine Learning Morphisms: A Framework For Designing And Analyzing Machine Learning Work Ows, Applied To Separability, Error Bounds, And 30-Day Hospital Readmissions, Eric Zenon Cawi

McKelvey School of Engineering Theses & Dissertations

A machine learning workflow is the sequence of tasks necessary to implement a machine learning application, including data collection, preprocessing, feature engineering, exploratory analysis, and model training/selection. In this dissertation we propose the Machine Learning Morphism (MLM) as a mathematical framework to describe the tasks in a workflow. The MLM is a tuple consisting of: Input Space, Output Space, Learning Morphism, Parameter Prior, Empirical Risk Function. This contains the information necessary to learn the parameters of the learning morphism, which represents a workflow task. In chapter 1, we give a short review of typical tasks present in a workflow, as …

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Theses & Dissertations

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, …

Algorithms For Training Large-Scale Linear Programming Support Vector Regression And Classification, Pablo Rivas Perea

Open Access Theses & Dissertations

The main contribution of this dissertation is the development of a method to train a Support Vector Regression (SVR) model for the large-scale case where the number of training samples supersedes the computational resources. The proposed scheme consists of posing the SVR problem entirely as a Linear Programming (LP) problem and on the development of a sequential optimization method based on variables decomposition, constraints decomposition, and the use of primal-dual interior point methods. Experimental results demonstrate that the proposed approach has comparable performance with other SV-based classifiers. Particularly, experiments demonstrate that as the problem size increases, the sparser the solution …

Doppler-Only Multistatic Radar, Dustin G. Mixon

Theses and Dissertations

In order to estimate the position and velocity of a target, most multistatic radar systems require multiple independent target measurements, such as angle-of-arrival, time-of-arrival, and Doppler information. Though inexpensive and reliable, Doppler-only systems have not been widely implemented due to the inherent nonlinear problem of determining a target’s position and velocity from their measurements. We solve this problem. In particular, we first establish the lack of observability in the Doppler-only bistatic system, thereby demonstrating the need for multiple transmitters and/or receivers. Next, for a multistatic system with a sufficient number of transmitter-receiver pairs, we invoke classical optimization techniques, such as …