Question

what is convex region​

Answer 1

Answer:

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• A Convex set is a region such that, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region.

Answer 2

Solution:-

❥In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points, it contains the whole line segment that joins them.

❥Equivalently, a convex set or a convex region is a subset that intersect every line into a single line segment (possibly empty).

❥ For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex.

❥ The boundary of a convex set is always a convex curve.

❥The boundary of a convex set is always a convex curve.

❥ The intersection of all the convex sets that contain a given subset A of Euclidean space is called the convex hull of A.

❥It is the smallest convex set containing A.

❥A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. 

❥Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

❥The branch of mathematics devoted to the study of properties of convex sets and convex functions is called convex analysis.