Subgradient

A subgradient of a convex function

f

at

x

g

such that

f (y) \geq f (x) + g^{T} (y - x)

for every

y

in the domain.

Table of contents
- Subgradient of the absolute value Subgradient
- Subgradient inequality Subgradient

Subgradient of the absolute value

The absolute value function has

\partial ∣ x ∣ = {{sgn x}, [- 1, 1], x \neq = 0, x = 0.

Subgradient inequality

A vector is a subgradient when its supporting affine function lies below the convex function.

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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 205 / 2 / d / Solution

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