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Inexact Newton-Type Optimization with Iterated Sensitivities

Rien Quirynen (rien.quirynen***at***gmail.com)
Sebastien Gros (grosse***at***chalmers.se)
Moritz Diehl (moritz.diehl***at***imtek.uni-freiburg.de )

Abstract: 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 an arbitrary 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 becomes considerably easier to implement than the adjoint based scheme. The applicability of these results is motivated, specifically for dynamic optimization. In addition, the numerical performance of a specific open-source implementation is illustrated.

Keywords: Newton-type methods, Optimization algorithms, Direct optimal control, Collocation methods

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )


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Entry Submitted: 06/21/2016
Entry Accepted: 06/21/2016
Entry Last Modified: 01/22/2017

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