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**Harvard**

Verschueren, R., Zanon, M., Quirynen, R. och Diehl, M. (2017) *A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control*.

** BibTeX **

@article{

Verschueren2017,

author={Verschueren, R. and Zanon, Mario and Quirynen, R. and Diehl, M.},

title={A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control},

journal={Siam Journal on Optimization},

issn={1052-6234},

volume={27},

issue={3},

pages={2085-2109},

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 de finite 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.},

year={2017},

keywords={regularization, nonlinear predictive control, SQP, optimal control, model-predictive control, nonlinear mpc, sqp method, optimization, algorithm, solvers, Mathematics, hmid c, 1994, computers & chemical engineering, v18, p817 },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 252771

A1 Verschueren, R.

A1 Zanon, Mario

A1 Quirynen, R.

A1 Diehl, M.

T1 A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

YR 2017

JF Siam Journal on Optimization

SN 1052-6234

VO 27

IS 3

SP 2085

OP 2109

AB 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 de finite 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.

LA eng

DO 10.1137/16m1081543

LK http://dx.doi.org/10.1137/16m1081543

OL 30