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In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivatives.
Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding local minima or maxima. Finding an arbitrary local minimum is relatively straightforward by using classical local optimization methods. Finding the global minimum of a function is far more ...
where are the input samples and () is the kernel function (or Parzen window). is the only parameter in the algorithm and is called the bandwidth. This approach is known as kernel density estimation or the Parzen window technique. Once we have computed () from the equation above, we can find its local maxima using gradient ascent or some other optimization technique. The problem with this ...
A surface with two local maxima. (Only one of them is the global maximum.) If a hill-climber begins in a poor location, it may converge to the lower maximum. Hill climbing will not necessarily find the global maximum, but may instead converge on a local maximum. This problem does not occur if the heuristic is convex.
If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗. Similarly, the function has a local minimum point at x ∗, if f(x ∗) ≤ f(x) for all x in X within distance ε of x ∗.
In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find the local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point).
In mathematical morphology, the h-maxima transform is a morphological operation used to filter local maxima of an image based on local contrast information. First, all local maxima are defined as connected pixels in a given neighborhood with intensity level greater than pixels outside the neighborhood.
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1] It is named after the mathematician Joseph-Louis ...