Introductory Lectures On Convex Optimization PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introductory Lectures On Convex Optimization PDF full book. Access full book title Introductory Lectures On Convex Optimization.
Author | : Yurii Nesterov |
Publisher | : Springer Science & Business Media |
Total Pages | : 270 |
Release | : 2003-12-31 |
Genre | : Mathematics |
ISBN | : 9781402075537 |
Download Introductory Lectures on Convex Optimization Book in PDF, ePub and Kindle
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
Author | : Y. Nesterov |
Publisher | : Springer Science & Business Media |
Total Pages | : 253 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 144198853X |
Download Introductory Lectures on Convex Optimization Book in PDF, ePub and Kindle
It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
Author | : I͡U︡. E. Nesterov |
Publisher | : |
Total Pages | : 236 |
Release | : 2004 |
Genre | : Convex functions |
ISBN | : 9780004501444 |
Download Introductory Lectures on Convex Optimization Book in PDF, ePub and Kindle
Author | : Yurii Nesterov |
Publisher | : Springer |
Total Pages | : 589 |
Release | : 2018-11-19 |
Genre | : Mathematics |
ISBN | : 3319915789 |
Download Lectures on Convex Optimization Book in PDF, ePub and Kindle
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.
Author | : Yurii Nesterov |
Publisher | : |
Total Pages | : 260 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9781441988546 |
Download Introductory Lectures on Convex Optimization Book in PDF, ePub and Kindle
Author | : Stephen P. Boyd |
Publisher | : Cambridge University Press |
Total Pages | : 744 |
Release | : 2004-03-08 |
Genre | : Business & Economics |
ISBN | : 9780521833783 |
Download Convex Optimization Book in PDF, ePub and Kindle
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.
Author | : Aharon Ben-Tal |
Publisher | : SIAM |
Total Pages | : 500 |
Release | : 2001-01-01 |
Genre | : Technology & Engineering |
ISBN | : 0898714915 |
Download Lectures on Modern Convex Optimization Book in PDF, ePub and Kindle
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.
Author | : Giuseppe C. Calafiore |
Publisher | : Cambridge University Press |
Total Pages | : 651 |
Release | : 2014-10-31 |
Genre | : Business & Economics |
ISBN | : 1107050871 |
Download Optimization Models Book in PDF, ePub and Kindle
This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.
Author | : James Renegar |
Publisher | : SIAM |
Total Pages | : 124 |
Release | : 2001-01-01 |
Genre | : Mathematics |
ISBN | : 9780898718812 |
Download A Mathematical View of Interior-point Methods in Convex Optimization Book in PDF, ePub and Kindle
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.
Author | : Hoang Tuy |
Publisher | : Springer Science & Business Media |
Total Pages | : 346 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475728093 |
Download Convex Analysis and Global Optimization Book in PDF, ePub and Kindle
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.