Real functions Convex functions Concept
Convex function
Summary
A convex function on an interval is a function whose graph lies on or below each of its chords. Convex functions have increasing slopes, and they satisfy Jensen's inequality. The node convex function gives the precise definition.
Where this leads
21 pages build on this one.
- Non-negative least squares
- Hopf–Lax formula
- Log-modulus of a holomorphic function is subharmonic
- Proximal operator
- Brenier's theorem
- Convex functions of subharmonic functions
- Midpoint convex function
- Talagrand's concentration inequality
- Total variation denoising
- Bernstein–Doetsch theorem
- Displacement convexity
- Elastic net
- Newton's minimal resistance problem
- Hadamard three-circle theorem for subharmonic functions
- Hadamard three-circle theorem
- Lasso
- Jensen inequality as a functional inequality
- Hadamard's two-constants theorem
- Fenchel–Moreau theorem
- Sierpiński's theorem on measurable midpoint convex functions
- Orlicz space
Further reading
- Web https://en.wikipedia.org/wiki/Convex_function, lead section
About this page
| Tag | 07Q7CNM5WF |
|---|---|
| URI | m2://07Q7CNM5WF |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A51 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Special cases
Definitions
Used by
- Non-negative least squares
- Hopf–Lax formula
- Proximal operator
- Brenier's theorem
- Convex functions of subharmonic functions
- Midpoint convex function
- Talagrand's concentration inequality
- Total variation denoising
- Bernstein–Doetsch theorem
- Displacement convexity
- Elastic net
- Newton's minimal resistance problem
- Hadamard three-circle theorem for subharmonic functions
- Hadamard three-circle theorem
- Lasso
- Fenchel–Moreau theorem
- Sierpiński's theorem on measurable midpoint convex functions
- Orlicz space