The Sequential Quadratic Programming Method

Sequential (or Successive) Quadratic Programming (SQP) is a technique for the solution of Nonlinear Programming (NLP) problems. It is, as we shall see, an idealized concept, permitting and indeed necessitating many variations and modifications before becoming available as part of a reliable and efficient production computer code. In this monograph we trace the evolution of the SQP method through some important special cases of nonlinear programming, up to the most general form of problem. To fully understand these developments it is important to have a thorough grasp of the underlying theoretical concepts, particularly in regard to optimality conditions. In this monograph we include a simple yet rigorous presentation of optimality conditions, which yet covers most cases of interest. A nonlinear programming problem is the minimization of a nonlinear objective function f(x), x ∈ IR, of n variables, subject to equation and/or inequality constraints involving a vector of nonlinear functions c(x). A basic statement of the problem, useful for didactic purposes is