MINLP combines the challenges of integer programming (discrete decisions) and nonlinear programming (nonlinear relationships). General form: minimize f(x,y) subject to g(x,y) ≤ 0, h(x,y) = 0, x continuous, y integer. MINLP is extremely difficult - non-convex cases are NP-hard even to approximate. Solution approaches: (1) Branch-and-Bound with NLP subproblems; (2) Outer Approximation - linearize nonlinearities generating MILP master problems; (3) Generalized Benders Decomposition; (4) Hybrid methods. Convex MINLP is more tractable than non-convex. Applications: process synthesis, product design, energy systems optimization, and portfolio optimization with discrete trading. Solvers: BARON, SCIP, Couenne, ANTIGONE.