Convex conjugate functions, Fenchel’s inequality, subdifferentials and optimality

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

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