- Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems Felipe Álvarez(falvarezdim.uchile.cl) Jèrôme Bolte(boltemath.jussieu.fr) J. Frédéric Bonnans(Frederic.Bonnansinria.fr) Francisco Silva(silvacmap.polytechnique.fr) Abstract: We consider a quadratic optimal control problem governed by a nonautonomous affine differential equation subject to nonnegativity control constraints. For a general class of interior penalty functions, we show how to compute the principal term of the pointwise expansion of the state and the adjoint state. Our main argument relies on the following fact: If the control of the initial problem satisfies strict complementarity conditions for its Hamiltonian except for a finite number of times, the estimates for the penalized optimal control problem can be derived from the estimations of a related stationary problem. Our results provide several types of efficiency measures of the penalization technique: error estimations of the control for $L^s$ norms ($s$ in $[1,+\infty]$), error estimations of the state and the adjoint state in Sobolev spaces $W^{1,s}$ ($s$ in $[1,+\infty)$) and also error estimates for the value function. For the $L^1$ norm and the logarithmic penalty, the optimal results are given. In this case we indeed establish that the penalized control and the value function errors are of order $O(\eps|\log\eps|)$. Keywords: Optimal control \and interior-point algorithms \and sensitivity \and expansion of value function and solutions Category 1: Other Topics (Other ) Citation: Published as Rapport de Recherche INRIA RR 6863, March 2009. Download: [PDF]Entry Submitted: 03/04/2009Entry Accepted: 03/04/2009Entry Last Modified: 03/04/2009Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.