Simply put: Optimizing a function f(x,y,z), we simply take the gradients and follow them downhill/uphill to optimize the function. However, when any of the variable(s) has a constraint on it (i.e it should be less or greater than some value(s) or some g(x) under some range), then how do we achieve the optimization process? I have been trying for sometime, but not able to get the idea clearly.

Can some body explain on the similar lines?. Will be much thankful.

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    $\begingroup$ firstly gradient descent will only find local maxima and minima. If the constraint is some auxiliary function g(x) = 0, then i think a google search of "Lagrange multipliers" will answer your question $\endgroup$ – meh Oct 11 '15 at 1:54

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