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IMA Journal of Applied Mathematics 1978 21(1):67-81; doi:10.1093/imamat/21.1.67
© 1978 by Institute of Mathematics and its Applications
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On the Convergence of Some Constrained Minimization Algorithms Based on Recursive Quadratic Programming

M. C. BIGGS

Numerical Optimisation Centre, Hatfield Polytechnic Hatfield, Hertfordshire

This paper considers the convergence of the method of recursive equality quadratic programming (REQP) for constrained minimization. A theorem of Wolfe (1969) gives conditions on the search directions and step lengths used by a minimization algorithm which ensure that it will locate an unconstrained stationary point of a function. It is shown here that, under suitable circumstances, the iterations of REQP satisfy these conditions both with respect to the conventional penalty function P(x, r) and also with respect to the augmented penalty function proposed by Fletcher (1969) which has a minimum at the solution to the constrained problem. The behaviour of REQP in the neighbourhood of the solution is also considered, and it is shown that the algorithm is capable of superlinear convergence.


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