On the Convergence of Some Constrained Minimization Algorithms Based on Recursive Quadratic Programming

This paper considers the convergence of the method of recursiveequality quadratic programming (REQP) for constrained minimization.A theorem of Wolfe (1969) gives conditions on the search directionsand step lengths used by a minimization algorithm which ensurethat it will locate an unconstrained stationary point of a function.It is shown here that, under suitable circumstances, the iterationsof REQP satisfy these conditions both with respect to the conventionalpenalty function P(x, r) and also with respect to the augmentedpenalty function proposed by Fletcher (1969) which has a minimumat the solution to the constrained problem. The behaviour ofREQP in the neighbourhood of the solution is also considered,and it is shown that the algorithm is capable of superlinearconvergence.