Convex Analysis

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5 domain-specific abstractions whose origin domain is Convex Analysis.

• Convex conjugate — The supremum transform mapping an extended-real function on a vector space to the greatest affine lower-bound gap over its dual space.
• Indicator function (convex analysis) — An extended-real function that is zero on a selected set and positive infinity outside it, encoding membership as a hard optimization constraint.
• Proper Convex Function — An extended-real convex function whose effective domain is nonempty and which nowhere takes negative infinity, excluding the two degenerate functions that break convex-analytic operations.
• Subderivative — A supporting slope or covector that generalizes the derivative of a convex function at a point where an ordinary derivative may not exist.
• Supporting hyperplane — A hyperplane meeting a set while the entire set lies in one of the two closed half-spaces it bounds.