Sequential Quadratic Programming

Abstract

Sequential Quadratic Programming (SQP) is one of the most successful methods for the numerical solution of constrained nonlinear optimization problems. It relies on a profound theoretical foundation and provides powerful algorithmic tools for the solution of large-scale technologically relevant problems. We consider the application of the SQP methodology to nonlinear optimization problems (NLP) of the form minimize f (x) (4.1a) over x ∈ lR n subject to h(x) = 0 (4.1b) g(x) ≤ 0 , (4.1c) where f : lR n → lR is the objective functional, the functions h : lR n → lR m and g : lR n → lR p describe the equality and inequality constraints. The NLP (4.1a)-(4.1c) contains as special cases linear and quadratic program-ming problems, when f is linear or quadratic and the constraint functions h and g are affine. SQP is an iterative procedure which models the NLP for a given iterate x k