Inexact Newton-Type Optimization with Iterated Sensitivities
Journal article, 2018

This paper presents and analyzes an Inexact Newton-type optimization method based on Iterated Sensitivities (INIS). A particular class of Nonlinear Programming (NLP) problems is considered, where a subset of the variables is defined by nonlinear equality constraints. The proposed algorithm considers any problem-specific approximation for the Jacobian of these constraints. Unlike other inexact Newton methods, the INIS-type optimization algorithm is shown to preserve the local convergence properties and the asymptotic contraction rate of the Newton-type scheme for the feasibility problem, yielded by the same Jacobian approximation. The INIS approach results in a computational cost which can be made close to that of the standard inexact Newton implementation. In addition, an adjoint-free (AF-INIS) variant of the approach is presented which, under certain conditions, becomes considerably easier to implement than the adjoint based scheme. The applicability of these results is motivated, specifically for dynamic optimization problems. In addition, the numerical performance of a specific open-source implementation is illustrated.

Newton-type methods

collocation methods

optimization algorithms

direct optimal control

Author

Rien Quirynen

KU Leuven

Mitsubishi Electric Research Laboratories

Sébastien Gros

Chalmers, Electrical Engineering, Systems and control, Automatic Control

Moritz Diehl

University of Freiburg

SIAM Journal on Optimization

1052-6234 (ISSN) 1095-7189 (eISSN)

Vol. 28 1 74-95

Areas of Advance

Information and Communication Technology

Subject Categories

Mathematics

DOI

10.1137/16M1079002

More information

Latest update

9/4/2018 2