Abstract
Sequential quadratic programming (SQP) is a technique for nonlinear equality constrained minimization problems, which, from the point of view of local convergence, is equivalent to finding a root of the gradient of the Lagrangian by Newton's method, if the second order sufficient conditions hold. For general, unstructured, finite dimensional problems the size of the equation for the Newton step is reduced by means of an orthogonal factorization of the matrix of constraint gradients. In this paper we show how certain regularized parameter identification problems, which are posed in Hilbert space, can be solved by SQP without any need for orthogonal factorizations. This extends recent work of S. J. Wright and one of the authors (CTK). We discuss how certain nondegeneracy conditions can be verified in a general setting and the interpretation of sufficient conditions for quadratic convergence of the SQP iterates.
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