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mathematical optimization - Problem in finding the actual minimum of a rapidly varying function


I have been facing the problem of finding the true minimum of a rapidly varying functions. The commands like FindMinimum and NMinimize often lead to the minimum value which is the global minimum for that function. I try to present an example here:


y[x_] = Sin[10 x^2] + 5 Cos[20 x];

When I plot this function say in region {x,0,5}, I can see the minima which are lower in value than returned by the FindMinimum and NMinimize commands. Can anyone help to figure out what is going wrong here? Thanks.




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