An introduction to convexity, optimization, and algorithms
Heinz H. Bauschke, Walaa M. Moursi
Bok Engelsk 2024
| Omfang | sider
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|---|---|
| Opplysninger | 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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| Emner | Algorithms.
Convex domains. Mathematical optimization. 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.). |
| Dewey | |
| ISBN | 9781611977790
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