Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization

The paper studies 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 for equality constrained optimization. The present approach is to reformulate the problem into a univariate nonlinear equation ø(μ)=0 where the function ø(μ) is continuous, at least piecewise differentiable and monotone. Well-established methods then can be readily applied. The paper also considers an extension of the present approach to a class of non-convex quadratic functions and shows that the approach is applicable to reduce Hessian SQP algorithms. Numerical results are presented indicating that the present algorithm is reliable, robust and has the potential to be used as a building block to construct trust-region algorithms for small-sized problems in constrained optimization.