Computing a Celis-Dennis Tapia Trust Region Step for Equality Constrained Optimization

We study an approach for minimizing a convex quadratic function subject to two quadratic constraints. This problem stems from computing a trust region step for an SQP algorithm proposed by Celis, Dennis and Tapia (1984) for equality constrained optimization. Our approach is to reformulate the problem into a univariate nonlinear equation phi (mu) = 0 where the function phi (mu) is continuous, at least piecewise differentiable and monotonically decreasing. Well-established methods then can be readily applied. We also consider an extension of our approach to a class of non-convex quadratic functions and show that our approach is applicable to reduced Hessian SQP algorithms