Mathematical optimization Wikipedia.
Stochastic optimization is used with random noisy function measurements or random inputs in the search process. Infinite-dimensional optimization studies the case when the set of feasible solutions is a subset of an infinite dimensional space, such as a space of functions.

Optimization problem Wikipedia.
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete.: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.