In R there is a function nlm() which carries out a minimization of a function f using the Newton-Raphson algorithm. In particular, that function outputs the value of the variable code defined as follows:
code an integer indicating why the optimization process terminated.
1: relative gradient is close to zero, current iterate is probably solution.
2: successive iterates within tolerance, current iterate is probably solution.
3: last global step failed to locate a point lower than estimate. Either estimate is an approximate local minimum of the function or steptol is too small.
4: iteration limit exceeded.
5: maximum step size stepmax exceeded five consecutive times. Either the function is unbounded below, becomes asymptotic to a finite value from above in some direction or stepmax is too small.
Can someone explain me (maybe using a simple illustration with a function of only one variable) to what correspond situations 1-5?
For example, situation 1 might correspond to the following picture:
Thank you in advance!