Can a non-convex function have a global minimum?
A convex loss function has only one global minimum and no local minima, making it easier to solve with a simpler optimization algorithm.
However, a non-convex loss function has both local and global minima and requires an advanced optimization algorithm to find the global minimum..
Can convex functions have local minima?
It's actually possible for a convex function to have multiple local minima, but the set of local minima must in that case form a convex set, and they must all have the same value.
So, for instance, the convex function f(x)=max{‖x‖−1,0} has a minimum of 0 for all ‖x‖≤1..
Does convex function have local minima?
If f is strictly convex, then there exists at most one local minimum of f in X.
Consequently, if it exists it is the unique global minimum of f in X.May 29, 2018.
What is the difference between local and global minima?
A local minimum of a function is a point where the function value is smaller than at nearby points, but possibly greater than at a distant point.
A global minimum is a point where the function value is smaller than at all other feasible points..
- A local minimum of a function is a point where the function value is smaller than at nearby points, but possibly greater than at a distant point.
A global minimum is a point where the function value is smaller than at all other feasible points. - Because a local minimum θ in Rdθ only requires the θ to be locally optimal in Rdθ, it is nontrivial that the local minimum is guaranteed to achieve the globally optimality in Rdθ of the induced perturbable gradient basis model class.
- Strongly convex function There exists a unique local minimum which is also global.
For f differentiable, we say that x is a stationary point if ∇f(x)=0.
If f is differentiable at x and x is a local minimum, then x is stationary.
If f is convex and differentiable at x and x is stationary then x is a minimum.
