CONVEX FUNCTION Meaning and
Definition
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A convex function is a mathematical term that describes a function where the line segment joining any two points on its graph always lies above or on the graph. In other words, given any two points on a convex function's graph, the function output at any point along the connecting line segment between these two points will be less than or equal to the value of the function at the corresponding points.
More formally, a function f: R → R is said to be convex if, for any two points (x₁, f(x₁)) and (x₂, f(x₂)) on its graph, the function values along the line segment connecting these two points lie entirely above or on the graph. Mathematically, this can be expressed as:
f(tx₁ + (1-t)x₂) ≤ tf(x₁) + (1-t)f(x₂), for t ∈ [0,1]
In simpler terms, it implies that the function does not have any "dips" or concave regions, and its graph curves upward consistently. The concept of convexity is crucial in optimization theory, as it helps define the shapes of objective functions and constraints. Convex functions possess desirable properties, making them amenable to efficient optimization algorithms and guaranteeing global optima.
Common Misspellings for CONVEX FUNCTION
- xonvex function
- vonvex function
- fonvex function
- donvex function
- cinvex function
- cknvex function
- clnvex function
- cpnvex function
- c0nvex function
- c9nvex function
- cobvex function
- comvex function
- cojvex function
- cohvex function
- concex function
- conbex function
- congex function
- confex function
- convwx function
- convsx function
Etymology of CONVEX FUNCTION
The word "convex" originates from the Latin word "convexus", which means "arched" or "vaulted". In mathematics, specifically in convex analysis, a convex function is named as such because its graph is "arched" or "curved" upward, similar to the shape of a dome, bell or bow.
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