Sequential Quadratic Programming is an iterative method for nonlinear constrained optimization that solves a sequence of quadratic programming subproblems. At each iteration k: (1) approximate NLP by QP using second-order Taylor expansion of Lagrangian and first-order expansion of constraints; (2) solve QP to obtain search direction; (3) perform line search to ensure convergence; (4) update iterate and Hessian approximation (BFGS). SQP exhibits superlinear convergence under regularity conditions. It generalizes Newton's method to constrained problems. Modern implementations include: trust region variants, filter methods for globalization, and handling infeasible subproblems. SQP is the basis of solvers like SNOPT and successfully handles large-scale engineering design, optimal control, and process optimization problems.