Journal of Convex Analysis 09 (2002), No. 2, 543--561
Copyright Heldermann Verlag 2002
Sensitivity Analysis for Parametric Optimal Control of Semilinear Parabolic Equations
Kazimierz Malanowski
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland
kmalan@ibspan.waw.pl
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 Lp, 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.
Keywords: Parametric optimal control, semilinear parabolic equations, control constraints, Bouligand differentiability of the solutions.
MSC: 49K40; 49K20, 49K30
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