Disjunctive programming is a framework within mathematical optimization concerned with problems where the feasible region is defined by disjunctions (logical ORs) of simpler constraint sets, typically convex polyhedra. This approach allows for the direct modeling of logical conditions, combinatorial choices, and piecewise linear functions, providing a foundational basis for understanding and solving a broad range of complex optimization problems, including mixed-integer programming, through specialized techniques such as cutting plane methods.