Convex Optimization

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Convex Optimization

Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)

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Book Synopsis Convex Optimization by : Stephen P. Boyd

Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Convex Optimization Theory

Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529310
Total Pages : 256 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Convex Optimization Theory by : Dimitri Bertsekas

Download or read book Convex Optimization Theory written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2009-06-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Lectures on Convex Optimization

Author : Yurii Nesterov
Publisher : Springer
ISBN 13 : 3319915789
Total Pages : 589 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Lectures on Convex Optimization by : Yurii Nesterov

Download or read book Lectures on Convex Optimization written by Yurii Nesterov and published by Springer. This book was released on 2018-11-19 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

Convex Optimization in Normed Spaces

Author : Juan Peypouquet
Publisher : Springer
ISBN 13 : 3319137107
Total Pages : 124 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Convex Optimization in Normed Spaces by : Juan Peypouquet

Download or read book Convex Optimization in Normed Spaces written by Juan Peypouquet and published by Springer. This book was released on 2015-03-18 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.

Convex Optimization Algorithms

Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529280
Total Pages : 576 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Convex Optimization Algorithms by : Dimitri Bertsekas

Download or read book Convex Optimization Algorithms written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2015-02-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.

Algorithms for Convex Optimization

Author : Nisheeth K. Vishnoi
Publisher : Cambridge University Press
ISBN 13 : 1108633994
Total Pages : 314 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Algorithms for Convex Optimization by : Nisheeth K. Vishnoi

Download or read book Algorithms for Convex Optimization written by Nisheeth K. Vishnoi and published by Cambridge University Press. This book was released on 2021-10-07 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Convex Analysis and Optimization

Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529450
Total Pages : 560 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Convex Analysis and Optimization by : Dimitri Bertsekas

Download or read book Convex Analysis and Optimization written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2003-03-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including: 1) A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems. 2) A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization. 3) A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions. Among its features the book: a) Develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar b) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality c) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality d) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming e) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted at the publisher's web site http://www.athenasc.com/convexity.html

Statistical Inference Via Convex Optimization

Author : Anatoli Juditsky
Publisher : Princeton University Press
ISBN 13 : 0691197296
Total Pages : 655 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Statistical Inference Via Convex Optimization by : Anatoli Juditsky

Download or read book Statistical Inference Via Convex Optimization written by Anatoli Juditsky and published by Princeton University Press. This book was released on 2020-04-07 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences. Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems. Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

Convex Optimization of Power Systems

Author : Joshua Adam Taylor
Publisher : Cambridge University Press
ISBN 13 : 1107076870
Total Pages : 213 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Convex Optimization of Power Systems by : Joshua Adam Taylor

Download or read book Convex Optimization of Power Systems written by Joshua Adam Taylor and published by Cambridge University Press. This book was released on 2015-02-12 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous guide to convex optimization for power systems engineering.

Convex Analysis and Global Optimization

Author : Hoang Tuy
Publisher : Springer Science & Business Media
ISBN 13 : 1475728093
Total Pages : 346 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Convex Analysis and Global Optimization by : Hoang Tuy

Download or read book Convex Analysis and Global Optimization written by Hoang Tuy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.

Convex Analysis and Nonlinear Optimization

Author : Jonathan Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387312560
Total Pages : 316 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Convex Analysis and Nonlinear Optimization by : Jonathan Borwein

Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Lectures on Modern Convex Optimization

Author : Aharon Ben-Tal
Publisher : SIAM
ISBN 13 : 0898714915
Total Pages : 500 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Modern Convex Optimization by : Aharon Ben-Tal

Download or read book Lectures on Modern Convex Optimization written by Aharon Ben-Tal and published by SIAM. This book was released on 2001-01-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.

Convex Analysis for Optimization

Author : Jan Brinkhuis
Publisher : Springer Nature
ISBN 13 : 3030418049
Total Pages : 278 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Convex Analysis for Optimization by : Jan Brinkhuis

Download or read book Convex Analysis for Optimization written by Jan Brinkhuis and published by Springer Nature. This book was released on 2020-05-05 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

Convex Optimization for Signal Processing and Communications

Author : Chong-Yung Chi
Publisher : CRC Press
ISBN 13 : 1315349809
Total Pages : 294 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Convex Optimization for Signal Processing and Communications by : Chong-Yung Chi

Download or read book Convex Optimization for Signal Processing and Communications written by Chong-Yung Chi and published by CRC Press. This book was released on 2017-01-24 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Convex Optimization

Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
ISBN 13 : 9781601988607
Total Pages : 142 pages
Book Rating : 4.9/5 (886 download)

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Book Synopsis Convex Optimization by : Sébastien Bubeck

Download or read book Convex Optimization written by Sébastien Bubeck and published by Foundations and Trends (R) in Machine Learning. This book was released on 2015-11-12 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

Convex and Stochastic Optimization

Author : J. Frédéric Bonnans
Publisher : Springer
ISBN 13 : 3030149773
Total Pages : 311 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Convex and Stochastic Optimization by : J. Frédéric Bonnans

Download or read book Convex and Stochastic Optimization written by J. Frédéric Bonnans and published by Springer. This book was released on 2019-04-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.

Convex Optimization in Signal Processing and Communications

Author : Daniel P. Palomar
Publisher : Cambridge University Press
ISBN 13 : 0521762227
Total Pages : 513 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Convex Optimization in Signal Processing and Communications by : Daniel P. Palomar

Download or read book Convex Optimization in Signal Processing and Communications written by Daniel P. Palomar and published by Cambridge University Press. This book was released on 2010 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts provide the theoretical underpinnings of the subject plus tutorials on a wide range of applications, from automatic code generation to robust broadband beamforming. Emphasis on cutting-edge research and formulating problems in convex form make this an ideal textbook for advanced graduate courses and a useful self-study guide.