Sequential quadratic programming methods for large-scale problems

Sequential quadratic programming (SQP) methods are the method of choice when solving small or medium-sized problems. Since they are complex methods they are difficult (but not impossible) to adapt to solve large-scale problems. We start by discussing the difficulties that need to be addressed and then describe some general ideas that may be used to resolve these difficulties. A number of SQP codes have been written to solve specific applications and there is a general purpose SQP code called SNOPT, which is intended for general applications of a particular type. These are described briefly together with the ideas on which they are based. Finally we discuss new work on developing SQP methods using explicit second derivatives.