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Slope and Path Length

  • Ding-Zhu Du
  • Panos M. Pardalos
  • Weili Wu
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 56)

Abstract

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.

Keywords

Search Direction Line Search Feasible Region Global Convergence Constrain Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Ding-Zhu Du
    • 1
  • Panos M. Pardalos
    • 2
  • Weili Wu
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Center for Applied Optimization, ISE DepartmentUniversity of FloridaGainesvilleUSA

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