Basic Theory of Stochastic Optimization (original) (raw)

In this chapter we develop the basic theory of stochastic optimization. After some introductory remarks about the mathematical representation of uncertainty, we investigate the key ingredients of general stochastic programs, i.e. decision strategies, constraints, and objective functions. Subsequently, the static and dynamic versions of a stochastic optimization problem are formulated, and some elementary regularity conditions are discussed. Under these regularity conditions, the static and dynamic versions of the stochastic program at hand can be shown to be well-defined, solvable, and equivalent. Finally, we discuss two useful indicators, which enjoy wide popularity in literature: the expected value of perfect information (EVPI) represents the maximum amount to be paid in return for complete and accurate information about the future, whereas the value of the stochastic solution (VSS) quantifies the cost of ignoring uncertainty in choosing a decision.