An efficient method for finding the minimum of a function of several variables without calculating derivatives

By M. Powell. 1964

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

The Graph Neural Network Model (2009, positive): “In fact, (4) implements the Jacobi iterative method for solving nonlinear equations [55].”
Optimal polyhedral description of 3D polycrystals: Method and application to statistical and synchrotron X-ray diffraction data (2018, methodology): “Subplex is derived from the well-known Nelder-Mead simplex algorithm [45] and decomposes high-dimensional problems into a series of low-dimensional problems that can be handled by the simplex algorithm, while Praxis is derived from the direction-set method [46], which assumes a local quadratic form ”
A Gaussian approach for continuous time models of the short-term interest rate (2001, methodology): “The objective function (3.12) has no direct analytic expression for its derivatives with respect to since both the sampling frequency and the total number of sample observations depend on . Consequently, the numerical optimization is carried out using Powell’s conjugate direction algorithm ( Powell ”
A Review of Medical Image Registration (1993, methodology): “A search technique due to Powell 157] is used to nd the geometric transformation which, when applied to the \hat" coordinates, minimizes the mean squared distance between the \hat" points and the \head" surface.”
Theory and application of explicitly correlated Gaussians (2013, methodology): “There are a variety of optimization algorithms that can be adopted when energy gradients are available, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (Fletcher, 1987) or the conjugate gradient algorithm (Powell, 1964).”
Algorithms and applications for approximate nonnegative matrix factorization (2007, background): “Others (Powell, 1964, 1973; Zangwill, 1967) prove convergence for special classes of objective functions, such as convex quadratic functions.”
High Tide or Riptide on the Cosmic Shoreline? A Water-rich Atmosphere or Stellar Contamination for the Warm Super-Earth GJ 486b from JWST Observations (2023, methodology): “For each light curve, we first perform a least-squares minimization using the Powell method (Powell 1964) and then initialize our Markov chain Monte Carloroutine using our best-fit values.”
Privacy preserving regression modelling via distributed computation (2004, background): “Powell established the remarkable result that if f (β) is a quadratic function, then exactly p iterations of the iteration block would yield the exact minimizer of f (β)! (This involves solving p(p + 1) line minimization problems to obtain the minimizer of a quadratic function.) We refer the reader ”
Secure, Privacy-Preserving Analysis of Distributed Databases (2007, unknown): “This approach uses Powell’s derivativefree method for quadratic optimization problems (Powell 1964) to solve directly for β̂ = arg minβ (y − Xβ)T(y − Xβ).”