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Indeed, this randomization principle is known to be a simple and effective way to obtain algorithms with almost certain good performance uniformly across many data sets, for many sorts of problems. Stochastic optimization methods of this kind include: simulated annealing by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi (1983) [10] quantum annealing
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions .
The term stochastic process first appeared in English in a 1934 paper by Joseph L. Doob. [1] For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, [22] [23] though the German term had been used earlier in 1931 by Andrey Kolmogorov. [24]
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving linear systems when the collected data is corrupted by noise, or for approximating extreme values of functions which cannot be computed directly, but ...
The optimization of sequential experimentation is studied also in stochastic programming and in systems and control. Popular methods include stochastic approximation and other methods of stochastic optimization. Much of this research has been associated with the subdiscipline of system identification. [30]
The definition of a stochastic process varies, [67] but a stochastic process is traditionally defined as a collection of random variables indexed by some set. [ 68 ] [ 69 ] The terms random process and stochastic process are considered synonyms and are used interchangeably, without the index set being precisely specified.
Stochastic programming studies the case in which some of the constraints or parameters depend on random variables. Robust optimization is, like stochastic programming, an attempt to capture uncertainty in the data underlying the optimization problem. Robust optimization aims to find solutions that are valid under all possible realizations of ...
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. [ 1 ] Realizations of these random variables are generated and inserted into a model of the system.