convex,
adj. 1. (of a polygon) having no interior angle greater than 180°, so that all lines joining any pair of points on the boundary of the figure lie wholly inside it. Thus, in
the pentagon ADBFE is convex, but ACBFE is not. 2. (of a function) a. having the property that the chord joining any two points on its graph lies above the graph. Thus, with the usual orientation of the coordinate axes in the figure above, both ACB and AEFB are convex, although the polygon is not itself convex; ADB is not convex.
b. formally and more generally, such that for arguments x and y in the appropriate abstract space, and t in the interval [0, 1],
tf(x) + (1 - t)f(y) ≥ f(tx + (1 - t) y). 3. (of a set of points in a real vector space) having the property that if two points are in the set then so are all the points on the line segment joining them; this is, if x and y are any two points in the set, then so is tx + (1 - t)y, for all t between 0 and 1. Compare concave.
b. formally and more generally, such that for arguments x and y in the appropriate abstract space, and t in the interval [0, 1],
tf(x) + (1 - t)f(y) ≥ f(tx + (1 - t) y). 3. (of a set of points in a real vector space) having the property that if two points are in the set then so are all the points on the line segment joining them; this is, if x and y are any two points in the set, then so is tx + (1 - t)y, for all t between 0 and 1. Compare concave.