Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems

@article{Alvarez2012AsymptoticEF,
  title={Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems},
  author={Felipe Alvarez and J{\'e}r{\^o}me Bolte and J. Fr{\'e}d{\'e}ric Bonnans and Francisco J. Silva},
  journal={Math. Program.},
  year={2012},
  volume={135},
  pages={473-507}
}
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… CONTINUE READING
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