Math 2.0

definition

Strictly convex function

Definition

Let II be an interval and let f ⁣:I→Rf \colon I \to \mathbb{R} be a function. The function ff is strictly convex if f(tx+(1−t)y)<tf(x)+(1−t)f(y)f(t x + (1 - t) y) < t f(x) + (1 - t) f(y) for all x,y∈Ix, y \in I with x≠yx \ne y and all t∈(0,1)t \in (0, 1).

Remarks

Each strictly convex function is convex. A linear function is convex but not strictly convex. A strictly convex function has at most one minimum point. For example, x2x^2 and exe^x are strictly convex. Mathlib defines strict convexity as StrictConvexOn.

Explanations

L1 human

A strictly convex function bends upward everywhere, with no straight pieces in its graph. The chords lie strictly above the graph, except at their ends.

What this node needs for W1
  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 2 nodes in this order. The foundations come first, and the list ends with this node.

Convex function, definition, no evidence levelConvex functiondefinitionStrictly convex function, definition, no evidence levelStrictly convex funct…definition
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Convex function definition
  2. Strictly convex function definition

Sources

  1. Web https://en.wikipedia.org/wiki/Convex_function, Definition

What links here

No node links to this node yet.