Nonlinear programming (NLP) aims to solve optimization problems involving a nonlinear objective and constraint functions. Two methods, namely, sensitivity and barrier, are considered to be quite generalized to be able to successfully solve the NLP. The methods are designed for solving NLP involving large numbers of variables such as the power system. Since it is of practical importance, particular attention is given to the NLP that has the objective function and constraints described by quadratic forms. This type of problem is referred to as quadratic optimization. The special case where the constraints are of linear forms is known as quadratic programming (QP). Apart from being a very common form for many important problems, QP is also very important because many of the problems are often solved as a series of QP or sequential QP problems. Quadratic optimization is involved in power systems for maintaining a desirable voltage profile, maximizing power flow, and minimizing generation cost.