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)
Full text not available from this repository.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
| Item Type: | Article |
|---|---|
| Identification Number: | 10.1137/16M1081543 |
| Subjects: | T Technology > T Technology (General) |
| Research Area: | Computer Science and Applications |
| Depositing User: | Mario Zanon |
| Date Deposited: | 09 Mar 2018 14:12 |
| Last Modified: | 09 Mar 2018 14:12 |
| URI: | http://eprints.imtlucca.it/id/eprint/4008 |
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