The Lifted Newton Method and Its Application in Optimization

Abstract. We present a new “lifting” approach for the solution of nonlinear optimization problems (NLPs) that have objective and constraint functions with intermediate variables. Introducing these as additional degrees of freedom into the original problem, combined with adding suitable new constraints to ensure equivalence of the problems, we propose to solve this augmented system instead of the original system by a Newton-type method. This often offers advantages in terms of convergence rates and region of attraction. The main contribution of this article is an efficient algorithmic trick to generate the quantities needed for a Newton-type method on the augmented (“lifted”) system with (a) almost no additional computational cost per iteration compared to a nonlifted Newton method, and (b) with negligible programming burden. We derive lifted schemes for Newton’s method, as well as for constrained Gauss–Newton and adjoint based sequential quadratic programming (SQP) methods...

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Jan Albersmeyer, Moritz Diehl
• Keywords: Intermediate Variables, Nonlinear Optimization, Nonlinear Optimization Problems, SIAMJO 2010