The Search for Global Optimality

From the discussion in this chapter, it is clear that the difficulties associated with optimizing nonlinear problems are far greater than those for optimizing linear problems. For linear problems, finding the global optimum can, in principle, be guaranteed. 

In Chapter 1, an objective function for a nonlinear optimization was likened to the terrain in a range of 

When solving such nonlinear optimization problems, it is not desirable to terminate the search at a peak that is grossly inferior to the highest peak. The solution can be checked by repeating the search but starting from a different initial point. 

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