TY  - JOUR
SP  - 2085
N2  - 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
SN  - 1052-6234
PB  - Society for Industrial and Applied Mathematics
A1  - Verschueren, Robin
A1  - Zanon, Mario
A1  - Quirynen, Rien
A1  - Diehl, Moritz
IS  - 3
JF  - SIAM Journal on Optimization
UR  - http://doi.org/10.1137/16M1081543
Y1  - 2017///
AV  - none
TI  - A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control
VL  - 27
EP  - 2109
ID  - eprints4008
ER  -