Thread: Is Convexity Necessary for Lagrangian

I am trying to find the conditioned minima for f(x,y) given the constraint g(x,y).

For this to be a minima under the constraint, does f and g need to be convex?

Or do they just need to be continuous and non-zero first derivatives?

When is convexity necessary for optimization and when it isn't?


Thank you in advance

When is convexity necessary...

Don't know what you think, but for myself
I enjoy it when a minimization problem has a unique solution :P

and when it isn't?

When it isn't... Either the problem is geometrically obvious,
or requires extra machinery (such as quasiconvexity, rank-1 convexity, polyconvexity...).