[수학] convex, concave

 

convex

 

convex function

$$ tf(x)+(1-t)f(y) \geq f(tx+(1-t)y) $$

 

strictly convex function

$$ tf(x)+(1-t)f(y) > f(tx+(1-t)y) $$

https://blog.naver.com/sw4r/221148661854

https://hwiyong.tistory.com/7

concave

 

concave function

$$ tf(x)+(1-t)f(y) \leq f(tx+(1-t)y) $$

 

strictly concave function

$$ tf(x)+(1-t)f(y) < f(tx+(1-t)y) $$