octogenarian
发表于 2025-3-23 12:36:56
Fenchel Duality,We have already seen, in the First order sufficient condition (2.1.2), one benefit of convexity in optimization: critical points of convex functions are global minimizers. In this section we extend the types of functions we consider in two important ways:
你敢命令
发表于 2025-3-23 14:31:28
Special Cases,In our earlier section on theorems of the alternative (Section 2.2), we observed that finitely generated cones are closed. Remarkably, a finite linear-algebraic assumption leads to a topological conclusion. In this section we pursue the consequences of this type of assumption in convex analysis.
galley
发表于 2025-3-23 20:56:38
Fixed Points,Many questions in optimization and analysis reduce to solving a nonlinear equation . (.) = 0, for some function .: .. Equivalently, if we define another map . = . − . (where . is the identity map), we seek a point . in . satisfying . (.) = .; we call . a . of ..
直觉好
发表于 2025-3-23 22:53:38
https://doi.org/10.1007/978-1-4757-9859-3Mathematica; Microsoft Access; PostScript; boundary element method; constraint; convex analysis; duality; e
HUMP
发表于 2025-3-24 05:11:20
Springer Science+Business Media New York 2000
Soliloquy
发表于 2025-3-24 08:28:56
Jonathan M. Borwein,Adrian S. LewisReviews the increasingly sophisticated state of computational optimization techniques.Provides an accessible account of convex analysis and its applications and extensions.New Edition adds material on
Myocarditis
发表于 2025-3-24 10:52:10
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庄严
发表于 2025-3-24 15:45:19
Background,onal vector space over the reals ., equipped with an inner product ‹·,·›. We would lose no generality if we considered only the space .. of real (column) .-vectors (with its standard inner product), but a more abstract, coordinate-free notation is often more flexible and elegant.
Ankylo-
发表于 2025-3-24 19:19:55
Convex Analysis,ontinuous on the interior of their domains. Part of the surprise is that an . assumption (convexity) leads to a . conclusion (continuity). It is this powerful fact that guarantees the usefulness of regularity conditions like Adom . ∩ cont . ≠ ∅ (3.3.9), which we studied in the previous section.
Diuretic
发表于 2025-3-25 03:09:15
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