Stochastic optimization is a field of mathematical optimization that deals with optimizing objective functions which involve randomness or uncertainty. It incorporates probabilistic elements into standard optimization problems, making it suitable for problems where parameters are uncertain or subject to variability. In stochastic optimization, the objective function or constraints may depend on random variables, leading to a need to make decisions under uncertainty. This field aims to find the optimal solution that minimizes or maximizes the objective function while taking into account the probabilistic nature of the problem. Stochastic optimization techniques often involve using techniques from probability theory, stochastic processes, and optimization algorithms to find solutions that are robust and flexible in the face of uncertainty. This area of research has applications in a wide range of fields, including engineering, finance, operations research, and machine learning.