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Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates .
A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions. [1] [2] This framework contrasts with deterministic optimization, in which all problem parameters are assumed to be known exactly. The goal of stochastic programming is to find a decision which both ...
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. [1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability [ 2 ] but instead is a mathematical function in which
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]
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.
In a discrete-time context, the decision-maker observes the state variable, possibly with observational noise, in each time period. The objective may be to optimize the sum of expected values of a nonlinear (possibly quadratic) objective function over all the time periods from the present to the final period of concern, or to optimize the value of the objective function as of the final period ...
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.