Gaining Insight Into Convexity: Benefits & Applications

[latecoder]

My supervisor always talks about how a problem is convex or its nonconvex and we want to convexify it.

I understand that convexity gives a lot of advantages for optimization, and I understand the geometric definition of convexity.

How does my supervisor know something is convex? Like a segmentation of an image for instance. And what advantages does convexity give you.

 

[HallsofIvy]

Your supervisor is using non-standard terminology so no one but he/she can tell for certain what is meant. I suspect that there is some set of points inherent in the problem (the set of "feasible solutions" to a linear programming problem, for example) and he/she is referring to the convexity of that set.