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Convex Analysis and Nonlinear Optimization

2010-05-05 Mathematics
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Release : 2010-05-05
Genre : Mathematics
Kind : eBook
Book Rating : 560/5 ( reviews)

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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. This book was released on 2010-05-05. 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.

Convex Analysis and Nonlinear Optimization

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 598/5 ( reviews)

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Book Synopsis Convex Analysis and Nonlinear Optimization by : Jonathan M. Borwein

Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan M. Borwein. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: This book provides 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, since the main body of the text is self-contained, with each section rounded off by 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.

Convex Analysis and Optimization

2003-03-01 Mathematics
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Release : 2003-03-01
Genre : Mathematics
Kind : eBook
Book Rating : 450/5 ( reviews)

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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. This book was released on 2003-03-01. 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

Convex Optimization

2004-03-08 Business & Economics
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Release : 2004-03-08
Genre : Business & Economics
Kind : eBook
Book Rating : 783/5 ( reviews)

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Book Synopsis Convex Optimization by : Stephen P. Boyd

Download or read book Convex Optimization written by Stephen P. Boyd. This book was released on 2004-03-08. 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 Analysis and Nonlinear Optimization

2014-01-15
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Release : 2014-01-15
Genre :
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis Convex Analysis and Nonlinear Optimization by : Jonathan M. Borwein

Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan M. Borwein. This book was released on 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:

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