For u and v in a real vector space, a combination denoted by this term is the set "one minus lambda" times u plus "lambda times v," where lambda is between zero and one, and is a special case of an af⢄ne combination.
For u and v in a real vector space, a combination denoted by this term is the set "one minus lambda" times u plus "lambda times v," where lambda is between zero and one, and is a special case of an af⢄ne combination. Functions with this property have a positive semi-de⢄nite Hessian. If a function has this property on an interval, Jensen's inequality requires the function's value at the midpoint of the interval to be less than or equal to the average of the function's values at the endpoints. The set of all combinations denoted by this term forms a "hull" also denoted by it. It's possessed by a function if the second derivative is not negative on the interval "a comma b," or if a line segment connecting a and b lies above the function's graph. For 10 points, what property of a function is equivalent to being concave upward?
For u and v in a real vector space, a combination denoted by this term is the set "one minus lambda" times u plus "lambda times v," where lambda is between zero and one, and is a special case of an af⢄ne combination.
convex [or obvious equivalents, such as convexity; accept concave upward before "concave"; do not accept or prompt on "concave" or "concavity" or "concave down(ward)"]