convex envelope
The 'convex envelope' is a concept in mathematics and optimization theory, often used to simplify complex problems by transforming them into convex ones.
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Definition
C2Mathematics
(technical, academic)The smallest convex set that contains all points in a given set.
Example
- The convex envelope of a triangle's vertices is the triangle itself.
C2Optimization Theory
(technical, academic)The highest-valued convex function that underestimates or equals a given function over a set.
Example
- In optimization problems, the convex envelope can simplify the problem by replacing a nonconvex function with its convex counterpart.