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Stochastic optimization also include methods with random iterates. Some hybrid methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. [1] Stochastic optimization methods generalize deterministic methods for deterministic problems.
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 ...
Deterministic vs. stochastic [ edit ] Inventory optimization models can be either deterministic —with every set of variable states uniquely determined by the parameters in the model – or stochastic —with variable states described by probability distributions. [ 12 ]
Deterministic vs. probabilistic (stochastic). A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions.
Another significant application of stochastic processes in finance is in stochastic volatility models, which aim to capture the time-varying nature of market volatility. The Heston model [ 321 ] is a popular example, allowing for the volatility of asset prices to follow its own stochastic process.
In the literature, there are two types of MPCs for stochastic systems; Robust model predictive control and Stochastic Model Predictive Control (SMPC). Robust model predictive control is a more conservative method which considers the worst scenario in the optimization procedure.
Derivative-free optimization is a subject of mathematical optimization. This method is applied to a certain optimization problem when its derivatives are unavailable or unreliable. Derivative-free methods establish a model based on sample function values or directly draw a sample set of function values without exploiting a detailed model.
Stochastic dynamic programs can be solved to optimality by using backward recursion or forward recursion algorithms. Memoization is typically employed to enhance performance. However, like deterministic dynamic programming also its stochastic variant suffers from the curse of dimensionality.