@article{eprints4008,
         journal = {SIAM Journal on Optimization},
       publisher = {Society for Industrial and Applied Mathematics},
          author = {Robin Verschueren and Mario Zanon and Rien Quirynen and Moritz Diehl},
           title = {A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control},
            year = {2017},
          volume = {27},
           pages = {2085--2109},
          number = {3},
        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},
             url = {http://eprints.imtlucca.it/4008/}
}