An Introduction To Convex Optimization Theory And Applications

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An Introduction To Convex Optimization Theory And Applications

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-18

An Introduction To Convex Optimization Theory And Applications written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-18 with Mathematics categories.

ConvexOptimization is a powerful tool that has applications in a wide range of fields, including engineering, computer science, economics, statistics, and more. This book provides a clear and concise introduction to convexOptimization, making it a valuable resource for students, practitioners, and anyone else interested in learning more about this important topic. The book begins with an explanation of the basic building blocks of convex sets and functions. It then moves on to discuss optimality conditions and duality theory, which are essential tools for understanding and characterizing convexOptimization problems. The book also provides a detailed treatment of several important classes of convexOptimization problems, including linear, quadratic, and semidefinitOptimization problems. In addition to the core material, the book also includes a number of applications of convexOptimization to real-world problems. These applications are drawn from a wide range of fields, including engineering, computer science, economics, and statistics. The book also includes a number of end-of-chapel problems to help the reader test their understanding of the material. This book is an excellent resource for anyone interested in learning more about convexOptimization. It is written in a clear and concise style, and it provides a thorough treatment of the subject. The book is also very well-organized, making it easy for the reader to find the information they are looking for. Whether you are a student, a practitioner, or simply someone who is interested in learning more about convexOptimization, this book is a valuable resource. It provides a clear and concise introduction to the subject, and it is sure to help you develop a deep understanding of this powerful tool. If you like this book, write a review!

Convex Analysis And Nonlinear Optimization

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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Convex Analysis And Nonlinear Optimization written by Jonathan M. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.

New Perspectives In Operations Research And Management Science

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Author : Y. Ilker Topcu
language : en
Publisher: Springer Nature
Release Date : 2022-06-24

New Perspectives In Operations Research And Management Science written by Y. Ilker Topcu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-24 with Business & Economics categories.

This book presents innovative operations research applications in business, specifically industrial engineering and its sub-disciplines. It investigates new perspectives in operations research and management science with regard to research methods, the research context, and industrial engineering, offering readers a broad range of new approaches to management problems. The book features the latest work of researchers who have worked with Professor Fusun Ulengin or built upon her work in their academic careers. Written in honor of Prof. Ulengin, this book was edited by her former Ph.D. students, who are now experts in operations research, multiple criteria decision making, competitiveness, logistics, and supply chain management. Prof. Ulengin’s impact in academia is visible in the range of topics and methodologies featured in this book: Location and transportation problems, competitiveness of nations, food supply chains, debt collection, mathematical modelling, multiple criteria decision making, data envelopment analysis, random forests, and Bayesian networks.

Introduction To The Theory Of Nonlinear Optimization

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Author : Johannes Jahn
language : en
Publisher: Springer Nature
Release Date : 2020-07-02

Introduction To The Theory Of Nonlinear Optimization written by Johannes Jahn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Business & Economics categories.

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Convex Optimization Theory

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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2009-06-01

Convex Optimization Theory written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Mathematics categories.

An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).

Convex Optimization

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Author : Arto Ruud
language : en
Publisher: Nova Science Publishers
Release Date : 2019

Convex Optimization written by Arto Ruud and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.

Over the past two decades, it has been recognized that advanced image processing techniques provide valuable information to physicians for the diagnosis, image guided therapy and surgery, and monitoring of human diseases. Convex Optimization: Theory, Methods and Applications introduces novel and sophisticated mathematical problems which encourage the development of advanced optimization and computing methods, especially convex optimization.The authors go on to study Steffensen-King-type methods of convergence to approximate a locally unique solution of a nonlinear equation and also in problems of convex optimization. Real-world applications are also provided.The following study is focused on the design and testing of a Matlab code of the Frank-Wolfe algorithm. The Nesterov step is proposed in order to accelerate the algorithm, and the results of some numerical experiments of constraint optimization are also provided.Lagrangian methods for numerical solutions to constrained convex programs are also explored. For enhanced algorithms, the traditional Lagrange multiplier update is modified to take a soft reflection across the zero boundary. This, coupled with a modified drift expression, is shown to yield improved performance.Next, Newton's mesh independence principle was used to solve a certain class of optimal design problems from earlier studies. Motivated by optimization considerations, the authors show that under the same computational cost, a finer mesh independence principle can be given than before.This compilation closes with a presentation on a local convergence analysis for eighth�order variants of Hansen�Patrick�s family for approximating a locally unique solution of a nonlinear equation. The radius of convergence and computable error bounds on the distances involved are also provided.

Convex Optimization For Signal Processing And Communications

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Author : Chong-Yung Chi
language : en
Publisher: CRC Press
Release Date : 2017-01-24

Convex Optimization For Signal Processing And Communications written by Chong-Yung Chi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Technology & Engineering categories.

Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications. In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals. With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.

Introduction To The Scenario Approach

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Author : Marco C. Campi
language : en
Publisher: SIAM
Release Date : 2018-11-15

Introduction To The Scenario Approach written by Marco C. Campi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-15 with Mathematics categories.

This book is about making decisions driven by experience. In this context, a scenario is an observation that comes from the environment, and scenario optimization refers to optimizing decisions over a set of available scenarios. Scenario optimization can be applied across a variety of fields, including machine learning, quantitative finance, control, and identification. This concise, practical book provides readers with an easy access point to make the scenario approach understandable to nonexperts, and offers an overview of various decision frameworks in which the method can be used. It contains numerous examples and diverse applications from a broad range of domains, including systems theory, control, biomedical engineering, economics, and finance. Practitioners can find "easy-to-use recipes," while theoreticians will benefit from a rigorous treatment of the theoretical foundations of the method, making it an excellent starting point for scientists interested in doing research in this field. Introduction to the Scenario Approach will appeal to scientists working in optimization, practitioners working in myriad fields involving decision-making, and anyone interested in data-driven decision-making.

Lectures On Stochastic Programming Modeling And Theory Third Edition

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Author : Alexander Shapiro
language : en
Publisher: SIAM
Release Date : 2021-08-19

Lectures On Stochastic Programming Modeling And Theory Third Edition written by Alexander Shapiro and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.

An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. Since these problems occur in vast, diverse areas of science and engineering, there is much interest in rigorous ways of formulating, analyzing, and solving them. This substantially revised edition presents a modern theory of stochastic programming, including expanded and detailed coverage of sample complexity, risk measures, and distributionally robust optimization. It adds two new chapters that provide readers with a solid understanding of emerging topics; updates Chapter 6 to now include a detailed discussion of the interchangeability principle for risk measures; and presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs. Lectures on Stochastic Programming: Modeling and Theory, Third Edition is written for researchers and graduate students working on theory and applications of optimization, with the hope that it will encourage them to apply stochastic programming models and undertake further studies of this fascinating and rapidly developing area.

Mathematical Theories Of Machine Learning Theory And Applications

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Author : Bin Shi
language : en
Publisher: Springer
Release Date : 2019-06-12

Mathematical Theories Of Machine Learning Theory And Applications written by Bin Shi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Technology & Engineering categories.

This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.