A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control
Journal article, 2017

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.

nonlinear mpc

SQP

model-predictive control

1994

v18

hmid c

algorithm

solvers

computers & chemical engineering

regularization

optimization

optimal control

Mathematics

nonlinear predictive control

sqp method

p817

Author

R. Verschueren

Mario Zanon

Chalmers, Signals and Systems, Systems and control, Mechatronics

R. Quirynen

M. Diehl

SIAM Journal on Optimization

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

Vol. 27 3 2085-2109

Subject Categories

Mathematics

DOI

10.1137/16m1081543

More information

Created

10/25/2017