Convex conjugate functions and Fenchel’s inequality Let be some function. The convex conjugate of (also know as the Fenchel transformation), is the function defined as Fenchel’s equality is the following statement: Theorem (Fenchel’s inequality). For any , The proof of Fenchel’s equality follows directly from the definition of the convex conjugate: A direct application of […]
Convex conjugate functions, Fenchel’s inequality, subdifferentials and optimality
“Is that to say we are against Free Trade? No, we are for Free Trade, because by Free Trade all economical laws, with their most astounding contradictions, will act upon a larger scale, upon the territory of the whole earth; and because from the uniting of all these contradictions in a single group, where they will stand face to face, will result the struggle which will itself eventuate in the emancipation of the proletariat.”
Karl Heinrich Marx · Marx-Engels Collected Works, Vol. VI, p. 290
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