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Record Nr. |
UNINA9910146304803321 |
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Autore |
Simons Stephen <1938-> |
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Titolo |
Minimax and Monotonicity / / by Stephen Simons |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1998 |
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ISBN |
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Edizione |
[1st ed. 1998.] |
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Descrizione fisica |
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1 online resource (XI, 172 p.) |
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Collana |
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Lecture Notes in Mathematics, , 1617-9692 ; ; 1693 |
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Classificazione |
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Disciplina |
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Soggetti |
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Functional analysis |
Operator theory |
System theory |
Control theory |
Mathematical optimization |
Calculus of variations |
Functional Analysis |
Operator Theory |
Systems Theory, Control |
Calculus of Variations and Optimization |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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Functional analytic preliminaries -- Multifunctions -- A digression into convex analysis -- General monotone multifunctions -- The sum problem for reflexive spaces -- Special maximal monotone multifunctions -- Subdifferentials -- Discontinuous positive linear operators -- The sum problem for general banach spaces -- Open problems. |
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Sommario/riassunto |
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Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates |
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and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle. |
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