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visits member for 3 years, 8 months
seen Nov 14 at 20:06

Mar
16
comment Interval Algorithm for Gradient Descent Method
Yes, this algorithm should use interval arithmetic.
Feb
9
comment Existence of Saddle Point
I am just interested in real functions in $n$ independent variables.
Feb
9
comment Existence of Saddle Point
I realized that if I add one more condition then this example will not hold. I made the change above.
Feb
4
comment Existence of Saddle Point
Is there a condition I can add to make sure this example will not happen?
Feb
4
comment Existence of Saddle Point
Terrific! That answers my original question. I'm going to make an edit and add one more restriction to $g$ to eliminate this case.
May
31
comment Why is this function bounded and Lipschitz?
Not necessarily, but it turns out (almost always) that $g$ has finitely many critical points on $f \neq 0$. Plus I know each connected component of $f \neq 0$ has at least one local max.
May
31
comment Why is this function bounded and Lipschitz?
Intuitively all of these seem obvious. For example, $g$ should be bounded above by $\max g(c)$ where $c$ is a critical point of $g$. I feel like all of the proofs could be done by contradiction but I was looking for something more explicit (i.e., "this is the upper bound", or "this is the Lipschitz constant").