An introduction to convexity, optimization, and algorithms
Setting the stage -- Affine and convex sets -- Convex and lower semicontinuous functions -- More on convex and lower semicontinuous functions -- Global and local minimizers -- Even more on convex functions -- Support functions and polar cones -- Projection and separation -- Subgradients -- Normal c...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
2024
Philadelphia Mathematical Optimization Society 2024 |
| Schriftenreihe: | MOS-SIAM series on optimization
34 |
| Schlagworte: |
Convex domains
> Mathematical optimization
> Algorithms
> Numerical analysis -- Mathematical programming, optimization and variational techniques -- Optimization and variational techniques
> Numerical analysis -- Numerical methods in complex analysis (potential theory, etc.) -- Numerical methods in complex analysis (potential theory, etc.)
> Konvexe Analysis
> Optimierung
> Verallgemeinerte Gradientenmethode
> Karush-Kuhn-Tucker-Bedingungen
> Fenchels Dualitätssatz
> Algorithmus
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| Online Zugang: | Inhaltsverzeichnis |
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Tag hinzufügen | Zusammenfassung: | Setting the stage -- Affine and convex sets -- Convex and lower semicontinuous functions -- More on convex and lower semicontinuous functions -- Global and local minimizers -- Even more on convex functions -- Support functions and polar cones -- Projection and separation -- Subgradients -- Normal cones -- Directional and classical derivatives -- Subgradients, derivatives, and the Bregman distance -- Subgradient calculus -- Composition and maximum -- Minimizing a sum and the Fritz John necessary conditions -- Karush-Kuhn-Tucker conditions -- A worked-out KKT example -- Fenchel conjugates -- Biconjugates and Fenchel calculus -- Fenchel-Rockafellar duality -- Infimal convolution and conjugacy -- Nonexpansive operators -- Lipschitz continuity and smoothness -- Strong convexity -- Proximal mappings -- Prox decomposition -- Envelopes -- Subgradient methods -- The proximal gradient method -- The fast iterative soft thresholding algorithm (FISTA) -- Douglas-Rachford algorithm -- Peaceman-Rachford algorithm -- The product space trick. "Provides a comprehensive and accessible exploration of modern topics in convex analysis and optimization algorithms, with an emphasis on bridging the two areas"-- |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xv, 175 Seiten Illustrationen, Diagramme |
| ISBN: | 9781611977790 978-1-61197-779-0 |