difference between convex and concave functions

what is the difference between convex, non-convex, concave and non-concave functions? how will we come to know that the given function is convex or non-convex? and if a function is non-convex then it will necessarily be concave one?
Thanks in advance


A convex function has one minimum – a nice property, as an optimization algorithm won’t get stuck in a local minimum that isn’t a global minimum. Take x21, for example:Convex Function

A non-convex function is wavy – has some ‘valleys’ (local minima) that aren’t as deep as the overall deepest ‘valley’ (global minimum). Optimization algorithms can get stuck in the local minimum, and it can be hard to tell when this happens. Take x4+x32x22x, for example:enter image description here

A concave function is the negative of a convex function. Take x2, for example:Concave Function

A non-concave function isn’t a widely used term, and it’s sufficient to say it’s a function that isn’t concave – though I’ve seen it used to refer to non-convex functions. I wouldn’t really worry about this one.

Source : Link , Question Author : Honey , Answer Author : Avik Mohan

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