The traditional constrained optimization paradigm considers problems to be either deterministic (the values of all parameters are known with certainty) or stochastic (the value of at least one parameter is not known with certainty, but its probability distribution is known).We expand this paradigm by considering a third class of constrained optimization problems - problems for which the value of at least one parameter is not know with certainty and the probability distribution is not known, and so the value of the parameter is estimated using sample data. We also consider Bayesian and predictive approaches to these problems and bootstrap approaches to inference on the estimated maximand or minimand for such problems. We will also provide a few interesting examples.