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40 relations: Argonne National Laboratory, Berndt–Hall–Hall–Hausman algorithm, Broyden's method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Claude Lemaréchal, Davidon–Fletcher–Powell formula, Derivative, Function (mathematics), GNU Octave, Gradient, Hessian matrix, Interior-point method, Jacobian matrix and determinant, John Wiley & Sons, Limited-memory BFGS, Mathematical optimization, Maxima and minima, NAG Numerical Library, Newton's method, Newton's method in optimization, Norm (mathematics), Optimization Toolbox, Positive-definite matrix, Python (programming language), Quadratic function, Quasi-Newton inverse least squares method, Quasi-Newton least squares method, R (programming language), SciPy, Secant method, Sherman–Morrison formula, Stationary point, Symmetric rank-one, System of linear equations, Taylor series, Trust region, Underdetermined system, William C. Davidon, Wolfe conditions, Wolfram Mathematica.
Argonne National Laboratory
Argonne National Laboratory is a science and engineering research national laboratory operated by the University of Chicago Argonne LLC for the United States Department of Energy located near Lemont, Illinois, outside Chicago.
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Berndt–Hall–Hall–Hausman algorithm
The Berndt–Hall–Hall–Hausman (BHHH) algorithm is a numerical optimization algorithm similar to the Gauss–Newton algorithm.
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Broyden's method
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in variables.
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Broyden–Fletcher–Goldfarb–Shanno algorithm
In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems.
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Claude Lemaréchal
Claude Lemaréchal is a French applied mathematician, and former senior researcher (directeur de recherche) at INRIA near Grenoble, France.
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Davidon–Fletcher–Powell formula
The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition (see below).
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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GNU Octave
GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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Interior-point method
Interior-point methods (also referred to as barrier methods) are a certain class of algorithms that solve linear and nonlinear convex optimization problems.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
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Limited-memory BFGS
Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm using a limited amount of computer memory.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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NAG Numerical Library
The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group.
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Newton's method
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Newton's method in optimization
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to), also known as the stationary points of.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Optimization Toolbox
Optimization Toolbox is an optimization software package developed by MathWorks.
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Positive-definite matrix
In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.
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Python (programming language)
Python is an interpreted high-level programming language for general-purpose programming.
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Quadratic function
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.
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Quasi-Newton inverse least squares method
In numerical analysis, the quasi-Newton inverse least squares method is a quasi-Newton method for finding roots of functions of several variables.
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Quasi-Newton least squares method
In numerical analysis, the quasi-Newton least squares method is a quasi-Newton method for finding roots in variables.
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R (programming language)
R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.
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SciPy
SciPy (pronounced /ˈsaɪpaɪ'/ "Sigh Pie") is a free and open-source Python library used for scientific computing and technical computing.
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Secant method
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method.
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Sherman–Morrison formula
In mathematics, in particular linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of the sum of an invertible matrix A and the outer product, u v^T, of vectors u and v. The Sherman–Morrison formula is a special case of the Woodbury formula.
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Stationary point
In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.
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Symmetric rank-one
The Symmetric Rank 1 (SR1) method is a quasi-Newton method to update the second derivative (Hessian) based on the derivatives (gradients) calculated at two points.
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System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Trust region
Trust region is a term used in mathematical optimization to denote the subset of the region of the objective function that is approximated using a model function (often a quadratic).
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Underdetermined system
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns).
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William C. Davidon
William Cooper Davidon (March 18, 1927 – November 8, 2013) was an American professor of physics and mathematics, and a peace activist.
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Wolfe conditions
In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods, first published by Philip Wolfe in 1969.
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Wolfram Mathematica
Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.
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References
[1] https://en.wikipedia.org/wiki/Quasi-Newton_method
