eprintid: 4008
rev_number: 6
eprint_status: archive
userid: 87
dir: disk0/00/00/40/08
datestamp: 2018-03-09 14:12:55
lastmod: 2018-03-09 14:12:55
status_changed: 2018-03-09 14:12:55
type: article
metadata_visibility: show
creators_name: Verschueren, Robin
creators_name: Zanon, Mario
creators_name: Quirynen, Rien
creators_name: Diehl, Moritz
creators_id: 
creators_id: mario.zanon@imtlucca.it
creators_id: 
creators_id: 
title: A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control
ispublished: pub
subjects: T1
divisions: CSA
full_text_status: none
abstract: Quadratic programs (QP) with an indefinite Hessian matrix arise naturally in some direct optimal control methods, e.g., as subproblems in a sequential quadratic programming scheme. Typically, the Hessian is approximated with a positive definite matrix to ensure having a unique solution; such a procedure is called regularization. We present a novel regularization method tailored for QPs with optimal control structure. Our approach exhibits three main advantages. First, when the QP satisfies a second order sufficient condition for optimality, the primal solution of the original and the regularized problem are equal. In addition, the algorithm recovers the dual solution in a convenient way. Second, and more importantly, the regularized Hessian bears the same sparsity structure as the original one. This allows for the use of efficient structure-exploiting QP solvers. As a third advantage, the regularization can be performed with a computational complexity that scales linearly in the length of the control horizon. We showcase the properties of our regularization algorithm on a numerical example for nonlinear optimal control. The results are compared to other sparsity preserving regularization methods.


Read More: https://epubs.siam.org/doi/10.1137/16M1081543
date: 2017
publication: SIAM Journal on Optimization
volume: 27
number: 3
publisher: Society for Industrial and Applied Mathematics
pagerange: 2085-2109
id_number: doi:10.1137/16M1081543
refereed: TRUE
issn: 1052-6234
official_url: http://doi.org/10.1137/16M1081543
citation:   Verschueren, Robin and Zanon, Mario and Quirynen, Rien and Diehl, Moritz  A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control.  SIAM Journal on Optimization, 27 (3).  pp. 2085-2109.  ISSN 1052-6234      (2017)