Slope and Path Length
When you passed by a mountain, you may have noticed that the road somehow looks like a snake in s-shape. Why was the road built in such a way? The answer is easy, increase the length to decrease the slope. The longer its length is, the smaller its slope is. However, did you think that as its length approaches infinity its slope approaches zero (Figure 5.1)? In this chapter, we will use this idea to develop a tool to establish the global convergence of some algorithms.
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