James Rohal
Reputation
Next privilege 250 Rep.
 Mar16 comment Interval Algorithm for Gradient Descent Method Yes, this algorithm should use interval arithmetic. Feb9 comment Existence of Saddle Point I am just interested in real functions in $n$ independent variables. Feb9 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. Feb4 comment Existence of Saddle Point Is there a condition I can add to make sure this example will not happen? Feb4 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. May31 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. May31 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").