I was solving a nonlinear equation in matlab using the function fsolve. Matlab says "the problem appears regular as measured by the gradient". In the definition of problem appears regular it is written that:
The problem appears to be regular means the size of the gradient of the sum of squares of function values is less than the OptimalityTolerance tolerance (1e-4*OptimalityTolerance for the Levenberg-Marquardt algorithm).
My questions are:
What does it mean for a problem to be regular? Is there a formal definition?
and
Is there an analytic way to prove that a nonlinear equation is regular?