Search results
Results from the WOW.Com Content Network
Nelder-Mead optimization in Python in the SciPy library. nelder-mead - A Python implementation of the Nelder–Mead method; NelderMead() - A Go/Golang implementation; SOVA 1.0 (freeware) - Simplex Optimization for Various Applications - HillStormer, a practical tool for nonlinear, multivariate and linear constrained Simplex Optimization by ...
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.
At the line search step (2.3), the algorithm may minimize h exactly, by solving ′ =, or approximately, by using one of the one-dimensional line-search methods mentioned above. It can also be solved loosely , by asking for a sufficient decrease in h that does not necessarily approximate the optimum.
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken.
The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.
The principal reason for imposing the Wolfe conditions in an optimization algorithm where + = + is to ensure convergence of the gradient to zero. In particular, if the cosine of the angle between and the gradient, = ‖ ‖ ‖ ‖ is bounded away from zero and the i) and ii) conditions hold, then ().
The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a minimization or a maximization.
Since BFGS (and hence L-BFGS) is designed to minimize smooth functions without constraints, the L-BFGS algorithm must be modified to handle functions that include non-differentiable components or constraints. A popular class of modifications are called active-set methods, based on the concept of the active set. The idea is that when restricted ...