If and the Hessian is -Lipschitz near a minimizer , thenThus a sufficiently close initial point has an error exponent that doubles at each iteration.
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Newton's method (or the Newton-Raphson method) is an iterative numerical technique used to find successively better approximations to the roots (or zeroes) of a real-valued function. In optimization, it is often used to find the local maxima and minima of functions. ### Principle of Newton's Method in Optimization The method employs the first and second derivatives of a function to find critical points where the function's gradient (or derivative) is zero.