joint work with Philip Gill, Anders Forsgren
We consider the formulation and analysis of an active-set method for convex quadratic programming that is guaranteed not to cycle. Numerical experiments are presented that illustrate the behavior of the method on some highly degenerate quadratic programs.
joint work with Anders Forsgren
We discuss Newton-like methods for approximately solving systems of nonlinear equations. Equivalence is shown between a Newton-like method with linearization of gradients to one with inverse Hessian approximations. We also discuss the relationship of these methods to other Newton-like methods as well as their potential use in higher-order methods. Finally we specialize to systems of nonlinear equations arising in interior-point methods.
joint work with Dominique Orban, Ding Ma
We reimplement the LANCELOT augmented Lagrangian method as a short sequence of nonlinearly constrained subproblems that can be solved efficiently by IPOPT and KNITRO, with warm starts on each subproblem. NCL succeeds on degenerate tax policy models that can't be solved directly. These models (and algorithm NCL) are coded in AMPL. A Julia implementation of NCL gives results for standard test problems.