A framework for proving global convergence for a class of nonlinear constraints infeasibility problem is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the simple sufficient reduction criteria where trial points are accepted provided there is a sufficient decrease in the constraints violation function. The proposed methods solve a sequence of quadratic programming subproblems for which effective software is readily available, and instead of using line search strategies that could converge to singular non-stationary points, the methods utilize trust region techniques to induce global convergence. The proof technique is presented in a fairly general context, allowing a range of specific algorithm choices associated with choosing the Hessian matrix representation and controlling the trust region radius.
Numerical Optimization Report, Department of Electrical Engineering, University of Malaya, Pantai Valley, Kuala Lumpur 50603, Malaysia November 2003, revised January 2004.