Abstract

Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in LpL^p, p finite) functions of the parameter. The differentials are characterized as the solutions of accessory linear-quadratic problems. A uniform second order expansion of the optimal value function is obtained, as a corollary.

Author information

Contact details are reproduced from the original publication and may be historical.

Kazimierz Malanowski

Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland

kmalan@ibspan.waw.pl

Keywords

  • Parametric optimal control
  • semilinear parabolic equations
  • control constraints
  • Bouligand differentiability of the solutions

Mathematics Subject Classification

49K40; 49K20, 49K30

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Suggested citation

K. Malanowski. “Sensitivity Analysis for Parametric Optimal Control of Semilinear Parabolic Equations.” Journal of Convex Analysis 9 (2002), No. 2, 543–561. https://doi.org/10.68381/jca09032

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press.