The Many Faces Of Degeneracy In Conic Optimization

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The Many Faces of Degeneracy in Conic Optimization

Author : Dmitriy Drusvyatskiy
Publisher :
ISBN 13 : 9781680833911
Total Pages : 93 pages
Book Rating : 4.8/5 (339 download)

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Book Synopsis The Many Faces of Degeneracy in Conic Optimization by : Dmitriy Drusvyatskiy

Download or read book The Many Faces of Degeneracy in Conic Optimization written by Dmitriy Drusvyatskiy and published by . This book was released on 2017 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Slater's condition - existence of a "strictly feasible solution" - is a common assumption in conic optimization. Without strict feasibility, first-order optimality conditions may be meaningless, the dual problem may yield little information about the primal, and small changes in the data may render the problem infeasible. Hence, failure of strict feasibility can negatively impact off-the-shelf numerical methods, such as primal-dual interior point methods, in particular. New optimization modeling techniques and convex relaxations for hard nonconvex problems have shown that the loss of strict feasibility is a more pronounced phenomenon than has previously been realized. In this text, we describe various reasons for the loss of strict feasibility, whether due to poor modeling choices or (more interestingly) rich underlying structure, and discuss ways to cope with it and, in many pronounced cases, how to use it as an advantage. In large part, we emphasize the facial reduction preprocessing technique due to its mathematical elegance, geometric transparency, and computational potential.

Operator Theory, Analysis and the State Space Approach

Author : Harm Bart
Publisher : Springer
ISBN 13 : 3030042693
Total Pages : 464 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Operator Theory, Analysis and the State Space Approach by : Harm Bart

Download or read book Operator Theory, Analysis and the State Space Approach written by Harm Bart and published by Springer. This book was released on 2018-12-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.

Reduction Methods in Semidefinite and Conic Optimization

Author : Frank Noble Permenter
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis Reduction Methods in Semidefinite and Conic Optimization by : Frank Noble Permenter

Download or read book Reduction Methods in Semidefinite and Conic Optimization written by Frank Noble Permenter and published by . This book was released on 2017 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conic optimization, or cone programming, is a subfield of convex optimization that includes linear, second-order cone, and semidefinite programming as special cases. While conic optimization problems arise in a diverse set of fields (including machine learning, robotics, and finance), efficiently solving them remains an active area of research. Developing methods that detect and exploit useful structure-such as symmetry, sparsity, or degeneracy-is one research topic. Such methods include facial and symmetry reduction, which have been successful in several applications, often reducing solve time by orders of magnitude. Nevertheless, theoretical and practical barriers preclude their general purpose use: to our knowledge, no solver uses facial or symmetry reduction as an automatic preprocessing step. This thesis addresses some of these barriers in three parts: the first develops more practical facial reduction techniques, the second proposes a more powerful and computationally efficient generalization of symmetry reduction (which we call Jordan reduction), and the third specializes techniques to convex relaxations of polynomial optimization problems. Throughout, we place emphasis on semidefinite programs and, more generally, optimization problems over symmetric cones. We also present computational results.

Euclidean Distance Matrices and Their Applications in Rigidity Theory

Author : Abdo Y. Alfakih
Publisher : Springer
ISBN 13 : 3319978462
Total Pages : 258 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Euclidean Distance Matrices and Their Applications in Rigidity Theory by : Abdo Y. Alfakih

Download or read book Euclidean Distance Matrices and Their Applications in Rigidity Theory written by Abdo Y. Alfakih and published by Springer. This book was released on 2018-10-13 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.

Semidefinite Optimization and Convex Algebraic Geometry

Author : Grigoriy Blekherman
Publisher : SIAM
ISBN 13 : 1611972280
Total Pages : 487 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman

Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Introduction to Nonlinear Optimization

Author : Amir Beck
Publisher : SIAM
ISBN 13 : 1611973651
Total Pages : 286 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Introduction to Nonlinear Optimization by : Amir Beck

Download or read book Introduction to Nonlinear Optimization written by Amir Beck and published by SIAM. This book was released on 2014-10-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

Computational Geometry

Author : Franco P. Preparata
Publisher : Springer Science & Business Media
ISBN 13 : 1461210984
Total Pages : 413 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Geometry by : Franco P. Preparata

Download or read book Computational Geometry written by Franco P. Preparata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Multiple View Geometry in Computer Vision

Author : Richard Hartley
Publisher : Cambridge University Press
ISBN 13 : 1139449141
Total Pages : 676 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Multiple View Geometry in Computer Vision by : Richard Hartley

Download or read book Multiple View Geometry in Computer Vision written by Richard Hartley and published by Cambridge University Press. This book was released on 2004-03-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

A Gentle Introduction to Optimization

Author : B. Guenin
Publisher : Cambridge University Press
ISBN 13 : 1139992996
Total Pages : 283 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis A Gentle Introduction to Optimization by : B. Guenin

Download or read book A Gentle Introduction to Optimization written by B. Guenin and published by Cambridge University Press. This book was released on 2014-07-31 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.

First-Order Methods in Optimization

Author : Amir Beck
Publisher : SIAM
ISBN 13 : 1611974984
Total Pages : 476 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis First-Order Methods in Optimization by : Amir Beck

Download or read book First-Order Methods in Optimization written by Amir Beck and published by SIAM. This book was released on 2017-10-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Generalized Principal Component Analysis

Author : René Vidal
Publisher : Springer
ISBN 13 : 0387878114
Total Pages : 590 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Generalized Principal Component Analysis by : René Vidal

Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Acceleration Methods

Author : Alexandre d'Aspremont
Publisher :
ISBN 13 : 9781680839289
Total Pages : 262 pages
Book Rating : 4.8/5 (392 download)

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Book Synopsis Acceleration Methods by : Alexandre d'Aspremont

Download or read book Acceleration Methods written by Alexandre d'Aspremont and published by . This book was released on 2021-12-15 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers recent advances in a range of acceleration techniques frequently used in convex optimization. Using quadratic optimization problems, the authors introduce two key families of methods, namely momentum and nested optimization schemes. These methods are covered in detail and include Chebyshev Acceleration, Nonlinear Acceleration, Nesterov Acceleration, Proximal Acceleration and Catalysts and Restart Schemes.This book provides the reader with an in-depth description of the developments in Acceleration Methods since the early 2000s, whilst referring the reader back to underpinning earlier work for further understanding. This topic is important in the modern-day application of convex optimization techniques in many applicable areas.This book is an introduction to the topic that enables the reader to quickly understand the important principles and apply the techniques to their own research.

Large-Scale Nonlinear Optimization

Author : Gianni Pillo
Publisher : Springer Science & Business Media
ISBN 13 : 0387300651
Total Pages : 297 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Large-Scale Nonlinear Optimization by : Gianni Pillo

Download or read book Large-Scale Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Predictive Control for Linear and Hybrid Systems

Author : Francesco Borrelli
Publisher : Cambridge University Press
ISBN 13 : 1107016886
Total Pages : 447 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Predictive Control for Linear and Hybrid Systems by : Francesco Borrelli

Download or read book Predictive Control for Linear and Hybrid Systems written by Francesco Borrelli and published by Cambridge University Press. This book was released on 2017-06-22 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a simple approach that includes real-time applications and algorithms, this book covers the theory of model predictive control (MPC).

Geometry and Complexity Theory

Author : J. M. Landsberg
Publisher : Cambridge University Press
ISBN 13 : 110819141X
Total Pages : 353 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Geometry and Complexity Theory by : J. M. Landsberg

Download or read book Geometry and Complexity Theory written by J. M. Landsberg and published by Cambridge University Press. This book was released on 2017-09-28 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

Aspects of Semidefinite Programming

Author : E. de Klerk
Publisher : Springer Science & Business Media
ISBN 13 : 1402005474
Total Pages : 287 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Aspects of Semidefinite Programming by : E. de Klerk

Download or read book Aspects of Semidefinite Programming written by E. de Klerk and published by Springer Science & Business Media. This book was released on 2002-03-31 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming. In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.