Large Scale Convex Optimization

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Large Scale Convex Optimization

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Author : Ernest K. Ryu
language : en
Publisher: Cambridge University Press
Release Date : 2022-12

Large Scale Convex Optimization written by Ernest K. Ryu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12 with Mathematics categories.

A unified analysis of first-order optimization methods, including parallel-distributed algorithms, using monotone operators.

A Computional Study Of The Homogenous Algorithm For Large Scale Convex Optimization

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Author :
language : en
Publisher:
Release Date : 1996

A Computional Study Of The Homogenous Algorithm For Large Scale Convex Optimization written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.

Methods For Large Scale Convex Optimization Problems With L1 Regularization

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Author : Kwangmoo Koh
language : en
Publisher:
Release Date : 2008

Methods For Large Scale Convex Optimization Problems With L1 Regularization written by Kwangmoo Koh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Much of recent research in signal processing, statistics, and many other fields has focused on ℓ1 regularization based methods for feature selection, sparse signal reconstruction. In this thesis we study optimization problems with ℓ1 regularization, and efficient methods to solve them.

First Order Methods For Large Scale Convex Optimization

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Author : Zi Wang
language : en
Publisher:
Release Date : 2016

First Order Methods For Large Scale Convex Optimization written by Zi Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

The revolution of storage technology in the past few decades made it possible to gather tremendous amount of data anywhere from demand and sales records to web user behavior, customer ratings, software logs and patient data in healthcare. Recognizing patterns and discovering knowledge from large amount of data becomes more and more important, and has attracted significant attention in operations research (OR), statistics and computer science field. Mathematical programming is an essential tool within these fields, and especially for data mining and machine learning, and it plays a significant role for data-driven predictions/decisions and pattern recognition.The major challenge while solving those large-scale optimization problems is to process large data sets within practically tolerable run-times. This is where the advantages of first-order algorithms becomes clearly apparent. These methods only use gradient information, and are particularly good at computing medium accuracy solutions. In contrast, interior point method computations that exploit second-order information quickly become intractable, even for moderate-size problems, since the complexity of each factorization of a n n matrix in interior point methods is O(n^3). The memory required for second-order methods could also be an issue in practice for problems with dense data matrices due to limited RAM. Another benefit of using first-order methods is that one can exploit additional structural information of the problem to further improve the efficiency of these algorithms.In this dissertation, we studied convex regression, and multi-agent consensus optimization problems; and developed new fast first-order iterative algorithms to efficiently compute -optimal and -feasible solutions to these large-scale optimization problems in parallel, distributed, or asynchronous computation settings while carefully managing memory usage. The proposed algorithms are able to take advantage of the structural information of the specific problems we considered in this dissertation, and have strong capability to deal with large-scale problems. Our numerical results showed the advantages of our proposed methods over other traditional methods in terms of speed, memory usage, and especially communication requirements for distributed methods.

Cloud Radio Access Networks

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Author : Tony Q. S. Quek
language : en
Publisher: Cambridge University Press
Release Date : 2017-02-02

Cloud Radio Access Networks written by Tony Q. S. Quek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-02 with Computers categories.

The first book on Cloud Radio Access Networks (C-RANs), covering fundamental theory, current techniques, and potential applications.

Tools And Methods For Large Scale Convex Optimization

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Author : Eric Chu
language : en
Publisher:
Release Date : 2013

Tools And Methods For Large Scale Convex Optimization written by Eric Chu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Convex optimization is widely used in many areas of engineering science such as control theory, statistics and machine learning, and image and signal processing. There are, however, several barriers to the use of convex optimization in everyday engineering: solvers for convex optimization in general require specialized knowledge to code, and in order to solve problems, users must typically perform tedious manual transformations before calling a solver. This problem is exacerbated when problem sizes become extremely large. In this thesis, we investigate tools and methods to address these two issues in the context of large-scale convex optimization. In particular, we develop technology to handle very large problems, including a large-scale solver and a tool to model potentially large optimization problems. This tool allows users to describe their problems with an intuitive model that is automatically transformed into a form handled by the large-scale solver, liberating users from performing tedious manual transformations. For the large-scale solver, we use the alternating direction method of multipliers (ADMM) and express conic optimization problems in consensus form, splitting the linear algebra from the generalized conic inequalities. For modeling optimization problems, we present the quadratic cone modeling language (QCML), which like CVX is a tool that automatically converts convex optimization problems into conic form and solves them with a standard cone solver. Unlike CVX, QCML can be used to analyze and generate code for entire problem families without requiring another analysis or generation phase when problem (instance) data or dimensions change.

A Computational Study Of The Homogeneous Algorithm For Large Scale Convex Optimization

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Author : Erling D. Andersen
language : en
Publisher:
Release Date : 1996

A Computational Study Of The Homogeneous Algorithm For Large Scale Convex Optimization written by Erling D. Andersen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.

Novel Gradient Type Optimization Algorithms For Extremely Large Scale Nonsmooth Convex Optimization

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Author : Elena Olvovsky
language : en
Publisher:
Release Date : 2006

Novel Gradient Type Optimization Algorithms For Extremely Large Scale Nonsmooth Convex Optimization written by Elena Olvovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

A General Framework Of Large Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques

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Author : Soysal Degirmenci
language : en
Publisher:
Release Date : 2016

A General Framework Of Large Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques written by Soysal Degirmenci and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electronic dissertations categories.

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.

Proceedings Of The 1995 American Control Conference

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Author : American Automatic Control Council
language : en
Publisher:
Release Date : 1995

Proceedings Of The 1995 American Control Conference written by American Automatic Control Council and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Automatic control categories.