Newton's method can be applied to optimization by finding the roots of the function's derivative. Since the slope or derivative of a function is equal to zero at its maximum or minimum, locating these zeros identifies the optimum points.
Conditions: The function has a maximum or minimum at the point being considered.; The derivative exists at that point.
Newton's method can be applied to optimization by finding the roots of the function's derivative. Since the slope or derivative of a function is equal to zero at its maximum or minimum, locating these zeros identifies the optimum points.
Conditions: The function has a maximum or minimum at the point being considered.; The derivative exists at that point.
Newton's method might find an unintended root or optimum because there is no guarantee of which root the algorithm will find. Depending on the initial guess and the shape of the function, it may converge to a different zero or stationary point than intended, such as finding a minimum when looking for a maximum.
Conditions: The function has multiple relevant roots or stationary points.; The initial guess does not ensure selection of a particular target.
Newton's method might find an unintended root or optimum because there is no guarantee of which root the algorithm will find. Depending on the initial guess and the shape of the function, it may converge to a different zero or stationary point than intended, such as finding a minimum when looking for a maximum.
Conditions: The function has multiple relevant roots or stationary points.; The initial guess does not ensure selection of a particular target.