Nonlinear Programming deals with optimization problems where the objective function or constraints are nonlinear. General form: minimize f(x) subject to g(x) ≤ 0, h(x) = 0. Challenges include: multiple local optima, non-convexity, and lack of closed-form solutions. Solution approaches: gradient-based methods (Newton, quasi-Newton, SQP), penalty and barrier methods, trust region methods, and global optimization techniques. Optimality conditions: KKT conditions (necessary for local optima), second-order conditions (sufficient). Special cases: convex programming (tractable), quadratic programming. Applications span: engineering design, chemical process optimization, parameter estimation, and machine learning. Commercial solvers: SNOPT, IPOPT, KNITRO. Modern research focuses on: global optimization and mixed-integer nonlinear programming (MINLP).