Philippe L. Toint The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable … Read more
We consider numerical methods for finding (weak) second-order critical points for large-scale non-convex quadratic programming problems. We describe two new methods. The first is of the active-set variety. Although convergent from any starting point, it is intended primarily for the case where a good estimate of the optimal active set can be predicted. The second … Read more
The following is a list of all of the published and unpublished works on quadratic programming that we are aware of. Some are general references to background material, while others are central to the development of the quadratic programming methods and to the applications we intend to cover in our evolving book on the subject. … Read more
A mechanism for proving global convergence infilter-type methods for nonlinear programming is described. Such methods are characterized by their use of the dominance concept of multi objective optimization, instead of a penalty parameter whose adjustment can be problematic. The main point of interest is to demonstrate how convergence for NLP can be induced without forcing … Read more