Convex Analysis and Its Applications

effective domain of a multifunction K, denoted dom k , is the set {#e E|K(#) # 0}= dom k . ... Suppose that { k; k, , we 8} is a family of closed-convex-values measurable multifunctions from E to E. Then M(i) for all v in 8 and x in E, ...

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Author: A. Auslender

Publisher: Springer Science & Business Media

ISBN: 9783642482984

Category: Business & Economics

Page: 219

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Convex Analysis in General Vector Spaces

105(1), 185–191. Cârjä, O. (1998) Elements of nonlinear functional analysis, Editura Universităţii “Al.I.Cuza”, Iaşi. Romanian. Castaing, C. and Valadier, M. (1977) Convex analysis and measurable multifunctions, Springer-Verlag, Berlin.

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Author: C Zalinescu

Publisher: World Scientific

ISBN: 9789814488150

Category: Mathematics

Page: 388

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The primary aim of this book is to present the conjugate and subdifferential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions. Contents:Preliminary Results on Functional AnalysisConvex Analysis in Locally Convex SpacesSome Results and Applications of Convex Analysis in Normed Spaces Readership: Researchers in analysis (convex and functional analysis), optimization theory and mathematical economy. Keywords:

Fundamentals of Convex Analysis

Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics 580. Springer Verlag, Heidelberg, 1977. F.H. Clarke. Optimization and Nonsmooth Analysis. Wiley, 1983; reprinted by SIAM, 1983. H.G. Eggleston. Convexity.

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Author: Jean-Baptiste Hiriart-Urruty

Publisher: Springer Science & Business Media

ISBN: 9783642564680

Category: Mathematics

Page: 259

View: 253

This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.

Convex Analysis and Minimization Algorithms I

Bertsekas, D.P. : Convexification procedures and decomposition methods for nonconvex optimization problems. J. Optimization Th. Appl. 29,2 (1979) 169-197. 22. ... Castaing, C, Valadier, M.: Convex Analysis and Measurable Multifunctions.

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Author: Jean-Baptiste Hiriart-Urruty

Publisher: Springer Science & Business Media

ISBN: 9783540568506

Category: Mathematics

Page: 418

View: 821

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

Convex Analysis and Minimization Algorithms II

Bertsekas, D.P.: Convexification procedures and decomposition methods for nonconvex optimization problems. J. Optimization Th. Appl. 29.2 (1979) 169–197. ... Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions.

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Author: Jean-Baptiste Hiriart-Urruty

Publisher: Springer Science & Business Media

ISBN: 9783662064092

Category: Business & Economics

Page: 348

View: 382

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

D. Butnariu and A. N. Iusem, Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization, Kluwer, Dordrecht, 2000. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, vol.

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Author: Heinz H. Bauschke

Publisher: Springer Science & Business Media

ISBN: 9781441994677

Category: Mathematics

Page: 468

View: 962

This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is presented, that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, best approximation theory, and convex feasibility. The book is accessible to a broad audience, and reaches out in particular to applied scientists and engineers, to whom these tools have become indispensable.

Multifunctions and Integrands

[3] C. CASTAING and M. WALADIER : Convex analysis and measurable multifunctions, Lecture Notes in Mathematics n° 580, Springer-Verlag, Berlin 1977. [4] J. P. R. CHRISTENSEN : Topology and Borel structure, North-Holland, American, ...

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Author: G. Salinetti

Publisher: Springer

ISBN: 9783540390831

Category: Mathematics

Page: 240

View: 352