Duality in vector optimization
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Duality in vector optimization by Radu Ioan BoЕЈ

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Published by Springer in Dordrecht, New York .
Written in English

Subjects:

  • Dualität,
  • Mathematical optimization,
  • Vector spaces,
  • Vektoroptimierung,
  • Duality theory (Mathematics)

Book details:

Edition Notes

Includes bibliographical references (p. [385]-395) and index.

StatementRadu Ioan Boţ, Sorin-Mihai Grad, Gert Wanka
SeriesVector optimization, Vector optimization
ContributionsGrad, Sorin-Mihai, 1979-, Wanka, Gert
Classifications
LC ClassificationsQA402.5 .B67 2009
The Physical Object
Paginationxv, 400 p. ;
Number of Pages400
ID Numbers
Open LibraryOL25016148M
ISBN 103642028853
ISBN 109783642028854
LC Control Number2009932674
OCLC/WorldCa428028527

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This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones. This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are : Springer-Verlag Berlin Heidelberg. This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality by: The need for a book on duality in vector optimization comes from the fact that despite the large amount of papers in journals and proceedings volumes, no book mainly concentrated on this topic was available so far in the scienti?c landscape. There is a considerable presence of books, not all recent releases, on vector optimization in the Brand: Radu Ioan Bot; Sorin-Mihai Grad; Gert Wanka.

Get this from a library! Duality in vector optimization. [Radu Ioan Boţ; Sorin-Mihai Grad; Gert Wanka] -- This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to. From the reviews:"This book is dedicated to duality in vector optimization and is largely based on the contribution of the authors to this field. The book is divided into 7 chapters; it also contains a list of symbols and notations, an index of terms and a bibliography with titles. This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex Price: $

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However in general the optimal values of the primal and dual problems need not be equal.   In this paper the problem dual to a convex vector optimization problem is defined. Under suitable assumptions, a weak, strong and strict converse duality theorem are proved. In the case of linear mappings the formulation of the dual is refined such that well-known dual problems of Gale, Kuhn and Tucker [8] and Isermann [12] are generalized by this by: 2 The Practical Importance of Duality Duality arises in nonlinear (and linear) optimization models in a wide variety of settings. Some immediate examples of duality are in: • Models of electrical networks. The current flows are “primal vari-ables” and the voltage differences are the “dual variables” that arise in consideration of File Size: KB.   This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality : Radu Ioan Bot.