In describing the NLP solution strategy summarized in Figure 8.2, we noted that the fastest improvement in the objective function is obtained by moving from point A in a direction that is...

In describing the NLP solution strategy summarized in Figure 8.2, we noted that the fastest improvement in the objective function is obtained by moving from point A in a direction that is perpendicular to the level curve of the objective function. However, there are other directions that also result in improvements to the objective.

a. How would you describe or define the set of all directions that result in improvement to the objective?

b. How would your answer change if the level curve of the objective function at point A was nonlinear?