Secant Approximation Methods for Convex Optimization PDF Download
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Author: Cheng-Yan Kao
Publisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 344
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Book Description
Author: Cheng-Yan Kao
Publisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 344
Get Book Here
Book Description
Author: C. Y. Kao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: James Renegar
Publisher: SIAM
ISBN: 9780898718812
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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: Y. Nesterov
Publisher: Springer Science & Business Media
ISBN: 144198853X
Category : Mathematics
Languages : en
Pages : 253
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Book Description
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: Yurii Nesterov
Publisher: Springer Science & Business Media
ISBN: 9781402075537
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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:
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
In this paper, the authors develop a unified theory for establishing the local and q-superlinear convergence of the secant methods from the convex class that takes advantage of the structure present in the Hessian in constructing approximate Hessians. As an application of this theory, they show the local and q-superlinear convergence of any structured secant method from the convex class for the constrained optimization problem and the nonlinear least-squares problem. Particular cases of these methods are the SQP augmented scale BFGS and DFP secant methods for constrained optimization problems introduced by Tapia. Another particular case, for which local and q-superlinear convergence is proved for the first time here, is the Al-Baali and Fletcher modification of the structured BFGS secant method considered by Dennis, Gay, and Welsch for the nonlinear least-squares problem and implemented in the current version of the NL2SOL code.
Author: Nisheeth K. Vishnoi
Publisher: Cambridge University Press
ISBN: 1108633994
Category : Computers
Languages : en
Pages : 314
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Book Description
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.
Author: J. E. Dennis, Jr.
Publisher: SIAM
ISBN: 0898713641
Category : Mathematics
Languages : en
Pages : 390
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Book Description
A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.
Author: Roger Fletcher
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Author: Leo Liberti
Publisher: Springer
ISBN: 3319607928
Category : Mathematics
Languages : en
Pages : 141
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Book Description
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
