This reference textbook, first published in 1982 by Academic Press, remains the authoritative and comprehensive treatment of some of the most widely used constrained optimization methods, including the augmented Lagrangian/multiplier and sequential quadratic programming methods. Among its special features, the book: 1) treats extensively augmented Lagrangian methods, including an exhaustive analysis of the associated convergence and rate of convergence properties 2) develops comprehensively sequential quadratic programming and other Lagrangian methods 3) provides a detailed analysis of differentiable and nondifferentiable exact penalty methods 4) presents nondifferentiable and minimax optimization methods based on smoothing 5) contains much in depth research not found in any other textbook