Sequential quadratic programming

The sequential quadratic programming (sequential QP) algorithm is a generalization of Newton's method for unconstrained optimization in that it finds a step away from the current point by minimizing a quadratic model of the problem. A number of packages, including NPSOL, NLPQL, OPSYC, OPTIMA, MATLAB, and SQP, are founded on this approach. In its purest form, the sequential QP algorithm replaces the objective function with its quadratic approximation.