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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 ...
Simultaneous perturbation stochastic approximation (SPSA) is an algorithmic method for optimizing systems with multiple unknown parameters. It is a type of stochastic approximation algorithm. As an optimization method, it is appropriately suited to large-scale population models, adaptive modeling, simulation optimization, and atmospheric modeling.
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 ...
is the optimization variable. ‖ x ‖ 2 {\displaystyle \lVert x\rVert _{2}} is the Euclidean norm and T {\displaystyle ^{T}} indicates transpose . [ 1 ] The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function ( A x + b , c T x + d ) {\displaystyle (Ax+b,c^{T}x+d)} to lie in the second ...
Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), [1] are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates ...
SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD) is an optimization and sampling technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models.
where y is an n × 1 vector of observable state variables, u is a k × 1 vector of control variables, A t is the time t realization of the stochastic n × n state transition matrix, B t is the time t realization of the stochastic n × k matrix of control multipliers, and Q (n × n) and R (k × k) are known symmetric positive definite cost matrices.