Quasi-Newton Versions

Abstract

In this chapter we discuss the quasi-Newton versions of the algorithms presented in chapters 12, 13 and 15. Just as in the case of unconstrained problems (see § 4.4), the quasi-Newton approach is useful when one does not want to compute second order derivatives of the functions defining the optimization problem to solve. This may be motivated by various reasons, which are actually the same as in unconstrained optimization: computing second derivatives may demand too much human investment, or their computing time may be too important, or the problem dimensions may not allow the storage of Hessian matrices (in the latter case, limited-memory quasi-Newton methods will be appropriate). Generally speaking, quasi-Newton methods require more iterations to converge, but each iteration is faster (at least for equality constrained problems).