Asuman Ozdaglar's Books

Convex Analysis and Optimization

By: Dimitri Bertsekas,Angelia Nedic,Asuman Ozdaglar

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Convex Analysis and Optimization

By: Dimitri Bertsekas,Angelia Nedic,Asuman Ozdaglar

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

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Page Count

560

Publisher

Athena Scientific

Published Date

ISBN 10

1886529450

ISBN 13

9781886529458

Network Games

Theory, Models, and Dynamics

By: Ishai Menache,Asuman E. Ozdaglar

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Network Games

Theory, Models, and Dynamics

By: Ishai Menache,Asuman E. Ozdaglar

Traditional network optimization focuses on a single control objective in a network populated by obedient users and limited dispersion of information. However, most of today's networks are large-scale with lack of access to centralized information, consist of users with diverse requirements, and are subject to dynamic changes. These factors naturally motivate a new distributed control paradigm, where the network infrastructure is kept simple and the network control functions are delegated to individual agents which make their decisions independently ("selfishly"). The interaction of multiple independent decision-makers necessitates the use of game theory, including economic notions related to markets and incentives. This monograph studies game theoretic models of resource allocation among selfish agents in networks. The first part of the monograph introduces fundamental game theoretic topics. Emphasis is given to the analysis of dynamics in game theoretic situations, which is crucial for design and control of networked systems. The second part of the monograph applies the game theoretic tools for the analysis of resource allocation in communication networks. We set up a general model of routing in wireline networks, emphasizing the congestion problems caused by delay and packet loss. In particular, we develop a systematic approach to characterizing the inefficiencies of network equilibria, and highlight the effect of autonomous service providers on network performance. We then turn to examining distributed power control in wireless networks. We show that the resulting Nash equilibria can be efficient if the degree of freedom given to end-users is properly designed. Table of Contents: Static Games and Solution Concepts / Game Theory Dynamics / Wireline Network Games / Wireless Network Games / Future Perspectives

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Page Count

161

Publisher

Morgan & Claypool Publishers

Published Date

ISBN 10

1608454088

ISBN 13

9781608454082

Convex Analysis and Optimization

By: Dimitri Bertsekas,Angelia Nedic,Asuman Ozdaglar

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Convex Analysis and Optimization

By: Dimitri Bertsekas,Angelia Nedic,Asuman Ozdaglar

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N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

560

Publisher

Athena Scientific

Published Date

ISBN 10

1886529450

ISBN 13

9781886529458

Network Games

Theory, Models, and Dynamics

By: Ishai Menache,Asuman E. Ozdaglar

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Network Games

Theory, Models, and Dynamics

By: Ishai Menache,Asuman E. Ozdaglar

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

161

Publisher

Morgan & Claypool Publishers

Published Date

ISBN 10

1608454088

ISBN 13

9781608454082

Book's by Asuman Ozdaglar

Convex Analysis and Optimization

Convex Analysis and Optimization

Network Games

Network Games

Convex Analysis and Optimization

Convex Analysis and Optimization

Network Games

Network Games

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