Convex Analysis¶
Rockafellar, R. T. (1970). Convex Analysis. Princeton University Press.
Cited by¶
5 citations across 5 artifacts.
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Primes¶
- Constraint
- … and its 1951 independent rediscovery and extension by Kuhn and Tucker established the KKT necessary conditions for constrained nonlinear optimization, generalizing Lagrange's framework to inequality constraints and remaining the foundational result of modern optimization theory; Rockafellar's 1970 Convex Analysis
This sourceFoundational treatise on convex analysis: formalizes curvature direction (convex vs. concave) as the primary geometric distinction in functional response and develops the duality framework underlying modern convex theory.
- … and its 1951 independent rediscovery and extension by Kuhn and Tucker established the KKT necessary conditions for constrained nonlinear optimization, generalizing Lagrange's framework to inequality constraints and remaining the foundational result of modern optimization theory; Rockafellar's 1970 Convex Analysis
- Convexity
- Convexity unlocks several reusable inference patterns, each stated in terms of mixtures and chords rather than any substrate. Jensen's inequality — for convex \(f\), the expectation of \(f(X)\) is at least \(f\) of the expectation — is the single source of the AM–GM inequality, the entropy bound, log-sum inequalities in information theory, and risk-premium calculations in finance.
This sourceCanonical treatise on convex sets and functions — Jensen's inequality, the separating-hyperplane theorem, Carathéodory's theorem, and duality.
- Convexity unlocks several reusable inference patterns, each stated in terms of mixtures and chords rather than any substrate. Jensen's inequality — for convex \(f\), the expectation of \(f(X)\) is at least \(f\) of the expectation — is the single source of the AM–GM inequality, the entropy bound, log-sum inequalities in information theory, and risk-premium calculations in finance.
Domain-specific¶
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