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# Pattern search (optimization)

Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require a gradient. [1]

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

## Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

## Enrico Fermi

Enrico Fermi (29 September 1901 – 28 November 1954) was an Italian-American physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1.

## Golden-section search

The golden-section search is a technique for finding the extremum (minimum or maximum) of a strictly unimodal function by successively narrowing the range of values inside which the extremum is known to exist.

In mathematics, the gradient is a multi-variable generalization of the derivative.

## Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

## Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

## Los Alamos National Laboratory

Los Alamos National Laboratory (Los Alamos or LANL for short) is a United States Department of Energy national laboratory initially organized during World War II for the design of nuclear weapons as part of the Manhattan Project.

## Luus–Jaakola

In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function.

## 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.

## Michael J. D. Powell

Michael James David Powell (29 July 193619 April 2015) was a British mathematician, who worked in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

## Multidimensional analysis

In statistics, econometrics, and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions and measurements.

## Nicholas Metropolis

Nicholas Constantine Metropolis (Greek: Νικόλαος Μητρόπουλος, June 11, 1915 &ndash; October 17, 1999) was a Greek-American physicist.

## Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

## Random optimization

Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized and RO can hence be used on functions that are not continuous or differentiable.

## Random search

Random search (RS) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized, and RS can hence be used on functions that are not continuous or differentiable.

## Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

## References

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