I have searched " pseudoconvex" in wiki: https://en.wikipedia.org/wiki/Pseudoconvex_function
However,i still don't understand what is this,the wiki said every convex is pseudoconvex,but the converse is not true . So what is their main difference?can anyone explain it by a figure or easier explanation to me?like this video:https://www.youtube.com/watch?v=Fu13eypvDWc&list=PLy7eeFbqDbH3-6zDk3R2F6_-gLRKnv9Zp&index=3&t=260s
It is a generalisation of convexity.
A convex differentiable function satisfies $f(y)-f(x) \ge Df(x)(y-x)$, so if $Df(x)(y-x) \ge 0$ then clearly $f(y)-f(x) \ge 0$.
A pseudo-convex function is one that is differentiable and if $Df(x)(y-x) \ge 0$ then $f(y)-f(x) \ge 0$.
Hence any convex function is automatically pseudo-convex.