Abstract: We give a brief review on the probabilistically constrained optimization problem which is an important class of stochastic programming with wide applications in finance, management and engineering planning. We introduce the modeling of probabilistic constraints and summarize some important  solution methods including convex approximation, DC approach, scenario approach and integer programming approach. We also discuss some future research perspectives of the probabilistically constrained optimization problem.

Key words: stochastic programming, probabilistic constraints, approximation methods, integer programming approach